The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+148x^74+168x^75+631x^76+428x^77+734x^78+452x^79+843x^80+516x^81+744x^82+564x^83+684x^84+420x^85+523x^86+276x^87+412x^88+156x^89+235x^90+68x^91+100x^92+16x^93+43x^94+8x^95+11x^96+5x^98+5x^100+1x^104

The gray image is a linear code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 4.97 seconds.