The generator matrix

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

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+118x^26+216x^27+619x^28+372x^29+599x^30+362x^31+545x^32+428x^33+478x^34+108x^35+167x^36+44x^37+19x^38+2x^39+12x^40+4x^41+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 1.16 in 0.253 seconds.