The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 1 1 1 0 1 1 1 1 0 0 X X
0 1 0 0 0 0 0 0 0 0 0 0 X X 1 1 1 1 1 X+1 1 X X 1
0 0 1 0 0 0 0 0 X X 1 1 1 X+1 X+1 1 1 X X+1 X X 1 0 1
0 0 0 1 0 0 1 X 1 1 0 X+1 0 1 0 X X 0 1 X+1 0 X 0 X+1
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 0 X X+1 1 1 X+1 0 X+1 1 1 X+1
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X 1 X 1 X 0 X X+1 X+1 X 0

generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+78x^17+153x^18+214x^19+290x^20+314x^21+364x^22+392x^23+432x^24+458x^25+382x^26+304x^27+277x^28+230x^29+124x^30+48x^31+23x^32+8x^33+1x^34+2x^35+1x^44

The gray image is a linear code over GF(2) with n=48, k=12 and d=17.
This code was found by Heurico 1.10 in 0.296 seconds.