The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  X X^2+X  0  1  X  X  1  1  1  X X^2  1  1  1  1 X^2  0  0  0 X^2+X  0 X^2 X^2+X X^2+X  1  1  1  1  X  X  X  1  1  1  0  1  0  1  X  1  1 X^2  X X^2  1  1  0  1  0  1  1  1  0 X^2  0  1 X^2  1  1  1  1  1  0  X  X  1  0  1
 0  1  0  0  0  0  0  0 X^2  1  1 X^2+1  1  1  1  1 X^2+X X^2+X  1 X^2+X X+1 X+1 X^2+X  1  1 X^2+X X^2+X X^2+X+1  1  1 X^2+X  1  0 X^2  1  X  1  X X^2+X  X  1  1 X^2  1 X+1  0 X+1 X^2+X X^2+X+1  X X^2+1  1 X^2+1  X X^2+X  1  1 X^2+X+1  0 X^2  X X^2 X^2+X  0 X^2+X  1  1  1 X^2+X  0 X^2+X  1  0 X^2+X+1  0  1 X^2+X  0  0  1 X^2
 0  0  1  0  0  0  1  1  1  1 X^2+1 X^2  X X^2+1 X^2+1 X^2 X^2  0 X^2+X+1 X+1  X  1  1 X^2+X  0 X^2+1 X^2+X  1  1 X^2+X  1 X^2+X+1  1  1 X^2+X  1  0  X X^2+X  X  0 X+1  1 X^2+X X+1  1 X^2+1  0 X^2+X  1 X+1 X^2 X^2+X  1 X^2+X X^2+1  X X^2+X X+1  1 X^2+1  1  X X^2+1  X X+1  1 X^2+X+1 X+1  1  X  1 X^2+X X^2+X+1  X X^2+X  X X^2+X  1 X^2 X^2
 0  0  0  1  0  1  1 X^2 X^2+1 X^2 X^2+1  1 X^2 X+1 X^2+X X+1 X+1  1 X^2  1  0 X^2+X X^2+X+1 X^2+X X^2+1 X^2+X X^2+X  1  X  1  0 X^2+X+1  X X^2+X+1  0 X^2+1 X^2+X+1 X^2+X+1  X X^2+X+1 X^2+X+1 X^2+1  X X^2+X+1  0 X^2+X X^2  1  0 X^2+X+1 X^2+X+1  0  X  1  1  0  0 X+1 X^2+X+1  0  X X^2+1 X^2+X X+1 X^2+X+1 X^2+1  0 X^2+X+1 X^2+X X^2+X+1 X^2  0 X^2+X  X  X X^2+X  1 X^2 X+1  1 X^2
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  0  1  0 X+1 X^2 X^2+1 X^2+X+1  0 X^2+1  0 X+1  X X+1  X  1 X^2+X+1 X^2+X X^2+X+1  X X^2  0 X+1 X^2+1  1 X^2 X^2  1 X+1 X^2+1 X^2+X  0  1 X^2+X  0  X  0  X X^2+X+1 X^2  1 X^2+X  1 X^2+1 X+1  0 X^2+1  1  1 X^2+X X^2+1 X^2+X X^2+X+1 X+1  1  1 X^2+X+1 X+1  X X+1 X^2  X  1 X+1  0  0 X+1 X+1 X^2+X+1  1 X+1 X^2+X  X
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+146x^70+482x^71+1120x^72+1376x^73+2080x^74+2504x^75+3585x^76+3662x^77+4808x^78+4580x^79+5604x^80+5298x^81+5737x^82+4928x^83+5054x^84+3930x^85+3479x^86+2194x^87+1976x^88+1108x^89+801x^90+504x^91+335x^92+100x^93+63x^94+40x^95+15x^96+10x^97+6x^98+6x^100+2x^101+2x^109

The gray image is a linear code over GF(2) with n=324, k=16 and d=140.
This code was found by Heurico 1.13 in 66.9 seconds.