The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  1 X^2+X X^2+X  1  1  X  1  1 X^2+X X^2+X X^2  1  1  X  1  1 X^2+X  1 X^2  1 X^2+X X^2  X  1  1 X^2 X^2  1 X^2+X  1  1  1 X^2  1  0  1 X^2+X  1  1  1  X  1  X  1  1  1  1 X^2 X^2  1 X^2  1  X X^2+X X^2  X  X  X  1  X  1 X^2+X X^2+X  1  1 X^2+X  0  1
 0  1  0  0  0  1  1  1 X^2  1  1  0  1  1  0  X  X  1 X^2+1 X^2+X  1  1 X^2  1 X^2  0  0 X^2+X+1  1 X+1 X+1  1 X+1 X^2+X  X  1  1 X^2+X X^2+1  X  0  1 X^2  X X^2+X+1 X^2+X  1 X^2 X^2+X  1  0  1 X+1 X^2+1 X+1  0 X^2+X+1  1 X^2 X+1 X^2+1 X^2  1  X X^2  X X^2+X  1 X^2 X^2+X  X  1  1  X  0  X X^2+X  1  X  X  X  1 X^2
 0  0  1  0  1 X^2 X^2+1  1  1  0  1 X^2  1  0 X^2+1 X^2  1  X X^2+X X^2+1 X^2+1  X X^2+X X^2+1 X^2  1 X^2+X+1 X^2+1 X^2 X^2+X+1  X X^2+1  0  1 X^2 X+1  X  1 X^2+1 X^2+1  X  0 X^2+1 X^2  X  0 X^2+X  1 X^2 X^2+X  X X^2+X+1 X+1  0  1  1 X^2+X+1  0 X^2 X^2+1 X^2+X  X X+1 X^2+X X^2+X+1  1 X^2+X  1  1  1  1  0 X^2+X+1 X^2+X+1  X  X  X X^2 X^2+X+1  1  1 X^2+1 X^2+X
 0  0  0  1 X^2  0 X^2 X^2  1  1 X^2+1  1  1 X^2+1 X^2+1 X^2+X X+1 X^2  0  0 X^2+X+1 X+1 X^2+X+1  0  1 X^2+X X+1 X^2+X X^2+1 X^2+X+1 X^2+1  X X^2+X X^2+X X^2 X+1 X^2 X^2+1  X X^2+1  1 X^2+X+1 X+1  1 X^2 X+1  X X+1 X^2+1 X^2+X  0  0  0 X^2+X+1 X^2+1 X^2+X+1  X X^2 X+1 X^2+X+1 X^2+1  1 X^2+X  1  0  1 X+1  1 X+1  0  X X^2+X+1 X^2+X X+1  1  X  1 X^2+X  1 X^2+1  0  X 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+222x^77+314x^78+458x^79+381x^80+456x^81+323x^82+378x^83+250x^84+254x^85+204x^86+206x^87+138x^88+116x^89+89x^90+130x^91+62x^92+36x^93+13x^94+24x^95+12x^96+16x^97+4x^99+4x^100+4x^101+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 1.11 in 0.484 seconds.