The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  1 X^2+X  1  X  1  1  1 X^2 X^2+X  0  1  1  1  1  1  1  1  X  X  1  X
 0  1  0  0  1 X^2+1  1  X  1 X+1 X^2+X+1  0 X^2  1  1 X^2+X  1  1  1 X^2+X X^2+1 X^2  1 X+1 X+1 X^2+1  1  1  1 X^2+1  1
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X X^2  1  1  X  1 X^2+X X+1 X^2+1 X^2+X+1 X^2+X+1  1  X X^2+X X+1 X^2+1  0 X^2+X  0 X^2 X^2  0 X^2+X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+158x^27+219x^28+382x^29+176x^30+296x^31+221x^32+260x^33+72x^34+118x^35+68x^36+62x^37+8x^38+4x^39+2x^40+1x^44

The gray image is a linear code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.16 in 35.1 seconds.