The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+46x^76+110x^77+222x^78+298x^79+289x^80+340x^81+358x^82+322x^83+314x^84+332x^85+333x^86+286x^87+216x^88+202x^89+165x^90+98x^91+49x^92+24x^93+20x^94+12x^95+6x^96+10x^97+16x^98+4x^99+6x^100+6x^101+4x^102+4x^103+1x^108+1x^110+1x^114

The gray image is a linear code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 1.52 seconds.