The generator matrix

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

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+128x^26+268x^27+515x^28+408x^29+536x^30+472x^31+534x^32+400x^33+410x^34+188x^35+145x^36+56x^37+28x^38+5x^40+2x^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 1.11 in 0.094 seconds.