The generator matrix

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

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+162x^74+36x^75+444x^76+152x^77+686x^78+288x^79+880x^80+360x^81+997x^82+376x^83+952x^84+360x^85+823x^86+288x^87+634x^88+152x^89+301x^90+36x^91+119x^92+72x^94+28x^96+19x^98+11x^100+11x^102+1x^106+1x^108+1x^112+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 24.3 seconds.