The generator matrix

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

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+235x^24+448x^25+1156x^26+1664x^27+2758x^28+3384x^29+4488x^30+4304x^31+4642x^32+3536x^33+2856x^34+1600x^35+1016x^36+376x^37+200x^38+48x^39+49x^40+4x^42+2x^44+1x^48

The gray image is a linear code over GF(2) with n=124, k=15 and d=48.
This code was found by Heurico 1.16 in 14.7 seconds.