The generator matrix
1 0 0 0 1 1 1 0 1 1 X 0 X 1 0 1 1 X 1 X X 0 1 X X 1 1
0 1 0 0 0 1 1 1 X+1 X 1 0 1 X 1 X+1 0 1 X+1 X 1 X X 1 X 1 0
0 0 1 0 1 1 0 1 1 0 X 1 1 X+1 X 0 0 1 1 X X+1 X 1 0 1 X+1 0
0 0 0 1 1 0 1 X+1 1 X+1 X+1 X+1 0 X X 0 X 0 1 1 1 1 X+1 X 0 1 0
0 0 0 0 X 0 0 X 0 X X 0 0 0 X X 0 X 0 X 0 X 0 X X X 0
0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 0 0
0 0 0 0 0 0 X 0 0 X X X 0 0 X 0 X X X X 0 0 0 0 X 0 0
generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+65x^20+76x^21+122x^22+156x^23+159x^24+184x^25+172x^26+200x^27+165x^28+188x^29+163x^30+140x^31+108x^32+64x^33+47x^34+16x^35+14x^36+7x^38+1x^42
The gray image is a linear code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.16 in 0.153 seconds.