The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 X 0 X X X X^2 X X^2 X X 1 1 1
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X 0 X^2+X X^2+X X X^2 X X^2 X X^2+X X 0 X^2 X X X X 0 X^2 0 0 X^2
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2
generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+6x^30+44x^31+7x^32+4x^35+2x^38
The gray image is a linear code over GF(2) with n=124, k=6 and d=60.
This code was found by Heurico 1.16 in 0.00949 seconds.