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.