The generator matrix

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

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+366x^29+192x^30+324x^31+180x^32+248x^33+114x^34+126x^35+45x^36+54x^37+12x^38+3x^40+4x^41+2x^42

The gray image is a linear code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.11 in 3.42 seconds.