The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+184x^26+200x^27+453x^28+384x^29+695x^30+408x^31+604x^32+352x^33+427x^34+152x^35+143x^36+32x^37+37x^38+8x^39+15x^40+1x^42

The gray image is a linear code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.16 in 0.39 seconds.