The generator matrix

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

generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+32x^68+38x^69+29x^70+46x^71+24x^72+20x^73+22x^74+16x^75+2x^76+4x^78+3x^80+4x^81+4x^82+2x^85+3x^86+2x^87+2x^90+2x^92

The gray image is a linear code over GF(2) with n=144, k=8 and d=68.
This code was found by Heurico 1.10 in 0 seconds.