The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+34x^25+68x^26+74x^27+217x^28+174x^29+360x^30+206x^31+370x^32+158x^33+200x^34+102x^35+44x^36+18x^37+8x^38+2x^39+4x^40+4x^42+3x^44+1x^48

The gray image is a linear code over GF(2) with n=124, k=11 and d=50.
This code was found by Heurico 1.16 in 28.4 seconds.