The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  0  1  0  1 X^2  1  0  1 X^2  1  0  X  1  1  X  1  1  1  0  1  0  1  X  1  1  X X^2  1  0  1  1 X^2  0  1  1  1  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X  X  0 X^2+X X^2  X  0  X  0 X^2 X^2+X X^2+X X^2  X  0  0 X^2+X X^2+X X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X  X  X X^2  0  X  0 X^2+X  0 X^2+X  X  0  X X^2+X X^2  0  X X^2+X  0  X  X X^2  X  0 X^2 X^2  0 X^2  0  X  0 X^2+X  X X^2+X X^2 X^2+X X^2 X^2 X^2 X^2+X X^2  X X^2 X^2+X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2 X^2  0 X^2 X^2  X  X  X X^2 X^2+X X^2  0  0  0  X X^2+X  X X^2+X X^2  X  0 X^2  0  0  0 X^2+X  X X^2+X X^2  X  0 X^2+X  X X^2 X^2  X  X X^2  X  0 X^2+X X^2+X X^2 X^2 X^2+X  X X^2 X^2  X X^2+X X^2  X  0 X^2+X X^2  X  0  X  0 X^2+X X^2+X  0  0 X^2  X X^2 X^2+X X^2+X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2 X^2 X^2+X X^2+X  X  X X^2 X^2+X  0 X^2 X^2 X^2  X  0 X^2+X X^2  X X^2+X  X  0  X  0 X^2+X X^2 X^2+X  0  0 X^2 X^2  X  0  0 X^2+X  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  0 X^2 X^2+X  0 X^2+X X^2  0  X X^2+X X^2+X  0  X X^2+X  0 X^2  X X^2+X X^2+X  X  X  0 X^2+X X^2+X X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  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 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  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+62x^73+120x^74+136x^75+177x^76+248x^77+265x^78+262x^79+353x^80+372x^81+317x^82+344x^83+305x^84+260x^85+233x^86+150x^87+123x^88+88x^89+61x^90+50x^91+48x^92+42x^93+26x^94+12x^95+14x^96+14x^97+2x^98+6x^99+2x^100+2x^101+1x^128

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 6.28 seconds.