The generator matrix

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

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+440x^78+696x^80+814x^82+696x^84+474x^86+413x^88+252x^90+141x^92+110x^94+33x^96+20x^98+2x^100+1x^104+2x^106+1x^108

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 26.7 seconds.