The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1  1  0 X^2+X X^2+X  1 X^2+X  1  1 X^2 X^2+X  1  1  0  1  X  1  1  1  X  1  1  0  1  1  X X^2+X X^2+X  1  1  1  0  1  1  1  1  1  X  0 X^2  1  1 X^2 X^2+X X^2+X  1  1  1  1  1  1  1  1  1  1  1  0  1 X^2+X  1  1 X^2  1  1  1  1 X^2+X  1  1  1 X^2+X  1
 0  1  0  0  1  1  1 X^2  1  1 X+1 X^2+X X^2+X+1  X  1  1  1  X  0  X X+1  1  1  1 X^2 X^2+X X^2+X+1  1  0 X^2 X^2+1  1 X^2+X X+1  1  X X^2+X+1  0  X  1 X^2+X+1 X^2+X  X  X X+1 X^2+X X+1 X^2+X X^2+1 X^2  1  0 X^2+1 X^2  1  X  1  X  0 X+1 X^2 X^2+X+1  1 X+1  1 X^2+X  X X^2  0  1  0  0 X+1  1 X+1  X X^2+1 X^2+1  1 X^2+X  0 X^2+X  1 X^2
 0  0  1 X+1 X^2+X+1  0 X+1  X  1  X  0  1  X  1 X^2+1  0 X+1  X  1 X^2+X+1 X^2+X+1  X X^2+1  X X^2+X  1  1 X+1 X^2+1  1 X^2+X X^2+X  0 X^2+1 X^2  X  X  1  1 X^2 X^2  1  1  1 X+1  1  1  0 X^2+X+1  1  1  1 X^2  0 X^2+X+1  1  X X+1  1 X+1 X^2 X^2 X^2+X X+1  X  X X^2+X X^2  1 X^2+1  1 X+1 X^2 X+1 X+1  X X^2 X^2  0 X^2+X+1  1 X^2+X+1 X^2 X^2+X
 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 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2  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 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  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+184x^76+128x^77+691x^78+292x^79+897x^80+312x^81+1017x^82+296x^83+951x^84+360x^85+859x^86+304x^87+654x^88+168x^89+420x^90+120x^91+259x^92+56x^93+135x^94+12x^95+44x^96+11x^98+13x^100+3x^102+4x^104+1x^108

The gray image is a linear code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 5.07 seconds.