The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1  1  1  1  1 X^2+X  0  1  1  1  0  0  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+1  1 X^2+X X+1  0 X+1 X^2+X X^2+1  1  1  0 X+1 X^2+X  X  1 X+1  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0

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+28x^22+110x^24+32x^25+276x^26+320x^27+632x^28+992x^29+1017x^30+1408x^31+995x^32+992x^33+625x^34+320x^35+276x^36+32x^37+90x^38+30x^40+10x^42+4x^44+1x^46+1x^50

The gray image is a linear code over GF(2) with n=124, k=13 and d=44.
This code was found by Heurico 1.16 in 1.22 seconds.