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 X^2+X  1 X^2+X X^2  1  1  X  1  1  1  1  1  0  1  0 X^2+X X^2  1  1  1  X X^2+X X^2  1  1  X  0  1  1  0  0  1  1  X  1 X^2  X X^2+X  1  X X^2+X X^2+X X^2  1 X^2+X X^2+X  1 X^2  1  0  0  1  0  1 X^2+X  X X^2  1 X^2  X  1 X^2+X
 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  1 X^2 X^2  0  0 X^2+X+1  1 X+1 X+1  X X+1 X^2+1  X X+1  1  1  1 X^2 X+1 X^2+1  1 X^2+X  1 X^2+X X+1  X  1  1 X^2+X  1  1  X  X  X X^2 X^2+X  0  1 X^2+X  1 X^2  1  X  X  1 X^2+X X^2+X+1  1 X^2+1  1  X X^2+X  X X^2+X  1  1  X X^2  X  1 X+1  X
 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+1 X^2+X X^2  1 X^2+X+1 X^2+1 X^2 X^2+X+1  X X+1  0 X^2+1  1  1 X^2+1 X+1  X X^2 X^2  X X+1 X^2+X  0 X^2+X+1 X+1  1 X^2+X  0  0 X+1  1 X^2+X X^2  1  X X^2 X^2+X  0  1 X^2+X+1  1 X^2+1 X^2+X X^2+X+1 X+1  0  1 X^2  X X^2+X+1  1 X^2+X  1 X^2+1  1 X^2+1  X X^2+X  1 X^2 X^2+X 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^2+X+1 X+1  0 X^2+X+1  1 X^2+X X+1 X^2+X X^2+1 X^2+X+1 X^2+1 X^2+1 X^2+X  X X^2+1 X^2+X+1  X X+1 X^2  X X+1 X^2+1 X^2  1 X^2+X+1  0  X  X  1 X+1 X^2+X+1 X^2+X+1 X+1  X  1  0 X^2  1  1 X+1  X X^2+X+1 X^2+1 X^2+1  1 X+1  1  1  0 X^2+X+1  X  1 X^2+X  0  0  1 X^2+X+1  1  1 X^2+1 X^2+X+1 X^2+X X+1  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+231x^78+300x^79+445x^80+390x^81+464x^82+354x^83+355x^84+264x^85+260x^86+160x^87+199x^88+162x^89+145x^90+74x^91+114x^92+44x^93+38x^94+24x^95+29x^96+4x^97+12x^98+16x^99+9x^100+1x^102+1x^106

The gray image is a linear code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.11 in 0.969 seconds.