The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1 X^2+X X^2 X^2 X^2+X  1 X^2+X  1  1  1  1  X X^2  1  1  1  1 X^2+X  1 X^2
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  0 X^2  1  1  1  1  1 X^2+1 X^2+X X^2+X X^2+X+1  0  X X^2 X^2+X+1  0 X^2+1  1 X+1  1
 0  0  1  0  1  1  0  1 X^2+1 X^2+X X^2+1  X  1 X+1  0 X^2 X^2+X X+1 X+1  0 X^2+1  X  1 X^2+X X+1 X^2  X X+1 X+1 X+1  X
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2 X^2+1 X^2+X+1  X X^2+1 X^2+X  X  0 X+1  0 X^2+X+1 X^2+X+1 X^2  1  0 X^2+X X^2+X  1  0  X X^2+X+1
 0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  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+229x^24+452x^25+1140x^26+1748x^27+2687x^28+3452x^29+4152x^30+4860x^31+4127x^32+3900x^33+2748x^34+1548x^35+1036x^36+388x^37+208x^38+36x^39+43x^40+8x^42+5x^44

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 14.5 seconds.