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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+182x^71+318x^72+404x^73+474x^74+436x^75+375x^76+320x^77+291x^78+214x^79+223x^80+194x^81+181x^82+122x^83+82x^84+100x^85+69x^86+44x^87+22x^88+22x^89+9x^90+10x^91+3x^92

The gray image is a linear code over GF(2) with n=308, k=12 and d=142.
This code was found by Heurico 1.11 in 0.406 seconds.