The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+42x^73+118x^74+116x^75+223x^76+214x^77+213x^78+308x^79+320x^80+356x^81+325x^82+336x^83+301x^84+308x^85+279x^86+216x^87+141x^88+98x^89+76x^90+44x^91+26x^92+6x^93+9x^94+4x^95+6x^96+1x^98+1x^100+1x^102+3x^104+1x^108+2x^110+1x^112

The gray image is a linear code over GF(2) with n=328, k=12 and d=146.
This code was found by Heurico 1.16 in 18.6 seconds.