The generator matrix

 1  0  0  0  0  1  1  1  1 X^2  1  X  1 X^2+X  1  X  1 X^2+X  X  1  X  X  1  X  1 X^2  1 X^2  0  1  1
 0  1  0  0  0  0  X  1 X^2+1  1  1  X  X  1 X^2+X+1  1  X  1  1  1  0 X^2 X^2 X^2+X X^2+1  1 X^2+X+1  1  1  X  0
 0  0  1  0  0  0 X+1  X X^2+1 X^2+X+1  0  1 X^2+X+1 X^2+X+1 X+1 X^2 X+1 X^2  X X^2+X  1  1  X  0  1 X^2+1  1  X  1 X^2  0
 0  0  0  1  0  1  1 X+1 X^2  1  0 X^2+1  X X^2+X X^2+1 X^2+1 X^2 X^2+1  0 X^2+1  X X^2+X+1 X^2  1 X+1  X  1 X+1 X+1 X+1  0
 0  0  0  0  1  1 X^2  0  X  X  1 X^2+1  1 X^2+X+1 X+1  0 X^2+X X+1  X X^2+1 X+1 X^2 X^2+X+1 X^2  0 X^2+X X^2+X+1 X^2+X X^2+X  1  0
 0  0  0  0  0  X  0  0  0  0 X^2  0 X^2  X X^2+X X^2 X^2+X X^2+X  X  X X^2  X X^2+X  X X^2 X^2+X X^2  X X^2 X^2+X  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+68x^22+378x^23+1126x^24+2150x^25+4219x^26+6544x^27+10752x^28+13564x^29+17428x^30+17998x^31+17876x^32+13944x^33+10904x^34+6520x^35+4055x^36+1988x^37+996x^38+358x^39+141x^40+34x^41+17x^42+8x^43+1x^44+2x^47

The gray image is a linear code over GF(2) with n=124, k=17 and d=44.
This code was found by Heurico 1.13 in 69.3 seconds.