The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2+X  0  1  1  0  1  1  1  1  X  1  1 X^2  X  1  1  X  1  1  X X^2+X  1  1  1  1  1  1  1 X^2+X  1 X^2  1  X  1  1  0  1  1  1  1 X^2+X  0  1  1  1  X  1  1 X^2+X  1  X  1  1  X  0  1  1  1  1  1 X^2  X  X X^2+X  0  1  1  1
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1 X^2+1  1  0  1 X^2+X  1  1  X  1  1 X+1 X^2+X+1 X^2 X^2+X  1  X X^2+1  1  1  1  X  1  1 X^2  1  1 X^2+X+1  0 X^2+X+1 X^2+1  1 X+1  X  1 X^2  1 X^2+X+1  1 X+1 X+1  1 X+1  0 X^2+X  X  1  1  0 X^2+X+1  1  1  X  X  1 X^2+X+1  1 X^2 X^2+1  1  1  X X+1 X+1 X^2+1  X  1  1  1  1  0  1 X^2+1 X^2+X
 0  0  X  0 X^2+X  0  0 X^2 X^2  0 X^2  X  0  X  X  X  X X^2+X  X  0 X^2+X X^2+X  0  X X^2+X X^2+X  X X^2  0 X^2  X X^2+X X^2+X  0 X^2 X^2+X  0 X^2 X^2 X^2+X  X  X X^2+X X^2  X  0 X^2 X^2 X^2  X  X  0 X^2+X X^2 X^2+X  0  X  0  X  X  X  X  0  0  0  0 X^2+X X^2+X X^2+X X^2  X  X  0 X^2  X  X  0 X^2  X  0 X^2+X X^2
 0  0  0  X  0  0  X X^2+X X^2+X X^2  X  X X^2+X X^2+X  X  X X^2  X  0  0  X X^2 X^2 X^2 X^2+X X^2+X  X X^2+X  X X^2+X X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  X  0 X^2 X^2 X^2+X  0  X X^2+X X^2+X  0 X^2+X X^2+X  0 X^2  0 X^2 X^2+X  0  X X^2 X^2+X X^2  X X^2+X  X  0 X^2  0  X  0 X^2+X  X X^2  0 X^2+X X^2+X  0  0 X^2+X  X X^2+X X^2  0
 0  0  0  0 X^2  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  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  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^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  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+74x^73+211x^74+274x^75+343x^76+446x^77+568x^78+566x^79+611x^80+728x^81+723x^82+702x^83+590x^84+582x^85+528x^86+408x^87+321x^88+180x^89+98x^90+74x^91+37x^92+26x^93+30x^94+18x^95+10x^96+8x^97+14x^98+6x^99+6x^100+2x^101+2x^102+1x^104+2x^105+1x^106+1x^114

The gray image is a linear code over GF(2) with n=328, k=13 and d=146.
This code was found by Heurico 1.16 in 51.4 seconds.