The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X 1 X X X X X X X 1 1
0 X 0 0 0 0 0 0 0 X X^2+X X^2+X X X^2+X X X^2+X X X^2+X X X^2 X^2+X X X^2+X X X 0 X^2 X X 0 X^2
0 0 X 0 0 0 X X^2+X X 0 0 X^2 X X^2+X X^2+X X 0 X^2 0 X X^2 0 X X^2+X X X^2+X 0 X^2+X X^2+X X^2+X X
0 0 0 X 0 X X X^2+X 0 X X X^2 0 X^2 X X^2+X X X X^2 X X^2 0 X^2+X X^2 0 0 0 X 0 X^2+X X
0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X X^2 X X^2+X 0 0 X X X^2+X 0 0 X^2 X X^2 X^2 X X^2 X X^2 X
0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0
0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2
0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2
generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+72x^22+126x^23+261x^24+348x^25+629x^26+818x^27+1244x^28+1554x^29+1845x^30+2474x^31+1911x^32+1594x^33+1327x^34+834x^35+616x^36+326x^37+202x^38+96x^39+57x^40+18x^41+19x^42+4x^43+4x^44+1x^46+2x^48+1x^50
The gray image is a linear code over GF(2) with n=124, k=14 and d=44.
This code was found by Heurico 1.16 in 6.43 seconds.