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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+294x^78+184x^79+591x^80+200x^81+602x^82+260x^83+511x^84+104x^85+348x^86+108x^87+249x^88+28x^89+216x^90+64x^91+160x^92+48x^93+58x^94+20x^95+22x^96+4x^97+14x^98+4x^99+1x^100+4x^102+1x^104

The gray image is a linear code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.16 in 1.94 seconds.