The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2  X  X  1  0  X  1  1 X^2  1  0  1 X^2
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X X^2 X^2+X X^2+X X^2+X  X  X X^2 X^2  X  X  X  X  X  0  X  0  X  0  0
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X X^2 X^2+X  0  0  0 X^2 X^2+X X^2 X^2+X X^2  X X^2+X  X  0  0 X^2+X  0  X
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X X^2+X  0  X X^2 X^2  X  X X^2 X^2  0 X^2 X^2+X X^2+X X^2+X X^2  0  0 X^2
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  0  X  X X^2  X X^2  X X^2  X  0 X^2  0  0  X  0  X X^2+X X^2+X  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+180x^26+52x^27+273x^28+112x^29+364x^30+184x^31+319x^32+112x^33+204x^34+52x^35+102x^36+84x^38+8x^40+1x^44

The gray image is a linear code over GF(2) with n=124, k=11 and d=52.
This code was found by Heurico 1.16 in 15.3 seconds.