The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  1 X^2  1  0  1 X^2+X  1  1  0  1  X  1  1  1  1  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X  1 X^2+1  0 X^2 X+1  1 X^2+X+1  1  X  1  1 X^2+X+1  1 X^2+X+1  X X^2+X X+1  0  0  X  0
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  0 X^2  X  0  X  X  0 X^2+X X^2  X X^2+X  0 X^2+X  X X^2  0  0  0  X  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 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+27x^22+80x^23+132x^24+184x^25+548x^26+418x^27+1885x^28+832x^29+3555x^30+1032x^31+3547x^32+864x^33+1904x^34+460x^35+543x^36+160x^37+97x^38+56x^39+32x^40+8x^41+12x^42+2x^43+3x^44+1x^46+1x^52

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 4.57 seconds.