The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+258x^77+279x^78+436x^79+360x^80+558x^81+246x^82+400x^83+225x^84+316x^85+137x^86+226x^87+127x^88+158x^89+56x^90+108x^91+47x^92+78x^93+35x^94+14x^95+8x^96+8x^97+14x^98+1x^102

The gray image is a linear code over GF(2) with n=332, k=12 and d=154.
This code was found by Heurico 1.16 in 22.7 seconds.