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.