The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1 X^2  1  1  1  1 X^2  1  X  0  1  1  1  X
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2  X X^2 X^2  X  0  0  0 X^2 X^2+X  X X^2+X X^2  X  0 X^2  0 X^2+X
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2 X^2+X  X X^2  X X^2  0 X^2+X X^2  0 X^2+X  0  X  X  X X^2  X
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X X^2+X X^2+X  0 X^2+X X^2  X X^2  X X^2+X  X  X  X  0  X  0  X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 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+31x^26+88x^27+98x^28+98x^29+137x^30+156x^31+132x^32+92x^33+77x^34+66x^35+18x^36+2x^37+7x^38+8x^39+6x^40+4x^42+2x^43+1x^48

The gray image is a linear code over GF(2) with n=124, k=10 and d=52.
This code was found by Heurico 1.16 in 0.0405 seconds.