The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+74x^23+253x^24+476x^25+1139x^26+1508x^27+2953x^28+3122x^29+4755x^30+3940x^31+5052x^32+3182x^33+2961x^34+1508x^35+1059x^36+446x^37+233x^38+74x^39+25x^40+6x^41+1x^56

The gray image is a linear code over GF(2) with n=124, k=15 and d=46.
This code was found by Heurico 1.16 in 16.5 seconds.