The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+34x^70+108x^71+148x^72+202x^73+227x^74+212x^75+239x^76+208x^77+203x^78+244x^79+239x^80+238x^81+212x^82+190x^83+205x^84+174x^85+149x^86+156x^87+140x^88+132x^89+106x^90+72x^91+61x^92+58x^93+38x^94+36x^95+20x^96+12x^97+23x^98+6x^99+3x^100

The gray image is a linear code over GF(2) with n=162, k=12 and d=70.
This code was found by Heurico 1.10 in 1.06 seconds.