The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+141x^24+60x^25+310x^26+220x^27+856x^28+748x^29+1260x^30+1036x^31+1302x^32+692x^33+776x^34+276x^35+340x^36+36x^37+84x^38+4x^39+43x^40+2x^42+4x^44+1x^48

The gray image is a linear code over GF(2) with n=124, k=13 and d=48.
This code was found by Heurico 1.16 in 1.32 seconds.