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

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+274x^24+414x^26+64x^27+806x^28+512x^29+1528x^30+896x^31+1719x^32+512x^33+700x^34+64x^35+465x^36+168x^38+62x^40+6x^42+1x^52

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 30.9 seconds.