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.