The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 0 X 1 1 1 1 1 1 1 1 0 1 0 1 1 X 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 1 1 0 X 1 1 1 X X+1 X X X 0 0 0 0 0 X X X X 0 0
0 0 1 1 1 0 1 0 1 X+1 X 0 1 1 1 0 X 1 X+1 1 1 1 X+1 X+1 0 1 0 1 1 X+1 0 1 0 0
0 0 0 X 0 0 0 0 0 X 0 X X X 0 0 X 0 X X 0 0 X X 0 0 0 X 0 X 0 X 0 0
0 0 0 0 X 0 0 0 0 0 0 X X X X 0 X 0 X X X X 0 0 0 X X X X X X X 0 0
0 0 0 0 0 X 0 0 0 0 X X X X 0 X 0 0 X X X 0 0 X X X 0 X 0 0 X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X 0 X 0 X 0 X X X X X 0 0 0 0 0 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X 0 X 0 X X 0 0 X X X 0 0 X X 0 0
0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 X X 0 X 0 0 0
generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+64x^24+24x^25+110x^26+104x^27+202x^28+208x^29+227x^30+304x^31+275x^32+384x^33+272x^34+384x^35+276x^36+304x^37+292x^38+208x^39+172x^40+104x^41+94x^42+24x^43+34x^44+24x^46+4x^50+1x^62
The gray image is a linear code over GF(2) with n=68, k=12 and d=24.
This code was found by Heurico 1.16 in 0.879 seconds.