The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+120x^74+124x^75+304x^76+324x^77+494x^78+584x^79+661x^80+664x^81+632x^82+704x^83+576x^84+664x^85+472x^86+600x^87+345x^88+312x^89+210x^90+100x^91+112x^92+20x^93+84x^94+40x^96+30x^98+7x^100+6x^102+1x^104+1x^116

The gray image is a linear code over GF(2) with n=332, k=13 and d=148.
This code was found by Heurico 1.16 in 6.01 seconds.