The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+152x^69+553x^70+1236x^71+1774x^72+2804x^73+3713x^74+5030x^75+6466x^76+7724x^77+9234x^78+9966x^79+10892x^80+11156x^81+11128x^82+10786x^83+9525x^84+7988x^85+6447x^86+4748x^87+3535x^88+2480x^89+1567x^90+1046x^91+497x^92+312x^93+152x^94+82x^95+44x^96+24x^97+4x^98+2x^99+2x^102+2x^104

The gray image is a linear code over GF(2) with n=324, k=17 and d=138.
This code was found by Heurico 1.13 in 263 seconds.