The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+102x^25+344x^26+402x^27+802x^28+784x^29+1124x^30+1034x^31+1261x^32+800x^33+752x^34+330x^35+262x^36+104x^37+52x^38+22x^39+10x^40+2x^41+4x^43

The gray image is a linear code over GF(2) with n=124, k=13 and d=50.
This code was found by Heurico 1.16 in 2.79 seconds.