The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  1  X  X  X  1  X  1  X  0  1  1 X^2  0  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X  0  X  0 X^2  X X^2+X  X  0 X^2+X X^2+X  X  0  X  X  X  X X^2 X^2 X^2
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X  X  0  X X^2+X  X  0  X  X X^2  0  X  0 X^2+X  0 X^2  X X^2  X
 0  0  0  X  X  0 X^2+X  X  0  X  0  X  X X^2 X^2+X X^2  X X^2+X X^2+X  X X^2 X^2  0 X^2+X X^2  0  0 X^2+X X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 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+123x^22+8x^23+412x^24+96x^25+834x^26+672x^27+1123x^28+1952x^29+1543x^30+2736x^31+1636x^32+1952x^33+1248x^34+672x^35+802x^36+96x^37+317x^38+8x^39+110x^40+30x^42+11x^44+1x^46+1x^48

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 9.29 seconds.