The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 X 1 X 1 1 1 1 1 X 1 X X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 0 X X X 2X 0 0 2X X X 2X 0 2X X 0 X X 2X 0 0 0 0 X 2X 2X X 0 0 0 X X 2X X 0 X 0 2X 0 2X 2X X 0 X X X X X X X 2X 0 X 0 0 2X X 0
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 X X 2X 2X 2X 2X 2X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 0 X 0 X X X 0 2X 0 0 X 2X X X 0 0 0 2X 0 0 X 2X 2X 2X 2X 2X 2X 0 X X 2X 0 2X X X X 0 2X X X
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X X 2X 2X 2X 0 X 0 2X 0 2X 0 2X X 0 X X X 0 2X 2X 0 0 X 0 0 X X 2X 2X X 2X 2X 0 X 2X 0 X X 0 X X 2X 0 2X 0 X 2X X X X 0
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 0 X 0 0 2X X X X 0 0 2X 0 2X 2X 0 2X 2X X X 2X X 0 X 2X X 0 2X 2X X X X 0 2X 0 0 0 0 2X 2X 0 X 0 0 X 2X 2X 0 0 0 2X 2X X 2X X 0 2X 2X 0
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 2X 2X X 0 0 2X 2X 2X 2X 0 0 2X X 0 0 2X 2X X 2X 0 X X 0 X 2X 0 2X 2X 0 X X X 0 X X 0 X 2X 0 0 0 0 X 0 X 0 0 X X 2X 0 0 0 2X 2X X X X
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X X 2X 0 0 X 2X 0 X 2X 2X X X 2X 2X X 0 2X X 0 X 0 0 X 2X X X X X 0 X X 0 2X 2X 0 2X 2X 0 0 0 2X 0 2X 0 X 0 0 0 2X 0 0 2X X X 2X 0 0 0
generates a code of length 84 over Z3[X]/(X^2) who´s minimum homogenous weight is 150.
Homogenous weight enumerator: w(x)=1x^0+96x^150+206x^153+218x^156+36x^157+220x^159+162x^160+180x^162+540x^163+210x^165+1170x^166+160x^168+1296x^169+152x^171+918x^172+170x^174+252x^175+110x^177+96x^180+100x^183+82x^186+72x^189+48x^192+28x^195+20x^198+10x^201+4x^204+2x^207+2x^231
The gray image is a linear code over GF(3) with n=252, k=8 and d=150.
This code was found by Heurico 1.16 in 1.81 seconds.