The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+48x^23+122x^24+190x^25+216x^26+352x^27+463x^28+824x^29+1238x^30+1248x^31+1287x^32+868x^33+434x^34+352x^35+215x^36+152x^37+90x^38+48x^39+22x^40+14x^41+6x^42+1x^44+1x^52

The gray image is a linear code over GF(2) with n=124, k=13 and d=46.
This code was found by Heurico 1.16 in 1.83 seconds.