The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+24x^72+58x^73+51x^74+46x^75+53x^76+64x^77+49x^78+22x^79+29x^80+18x^81+16x^82+16x^83+6x^84+16x^85+2x^86+6x^87+6x^88+2x^89+3x^90+2x^91+5x^92+5x^94+2x^95+4x^96+2x^97+2x^98+2x^103

The gray image is a linear code over GF(2) with n=156, k=9 and d=72.
This code was found by an older version of Heurico in 0 seconds.