The generator matrix

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

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+214x^78+373x^80+330x^82+352x^84+276x^86+249x^88+144x^90+64x^92+16x^94+9x^96+10x^98+6x^100+2x^102+1x^108+1x^116

The gray image is a linear code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.16 in 0.689 seconds.