The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1 X^2  1  1  1  1  X X^2  1  1  1  1  1  1  1  1  0  0  X  X
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  1  X X^2+1  1  0 X+1 X^2+1 X^2+X  1  1  0 X^2+1 X^2  0  X  X  1  0  0  1  1  1
 0  0  X  0 X^2+X  0  X X^2 X^2+X X^2+X  X X^2  X  0  0 X^2 X^2 X^2+X  0  0  X  X X^2+X  X X^2+X X^2+X  X  X X^2 X^2+X  X
 0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  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+72x^26+124x^27+204x^28+244x^29+264x^30+296x^31+236x^32+248x^33+154x^34+92x^35+59x^36+20x^37+20x^38+11x^40+2x^42+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 0.0934 seconds.