The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0 X^2+X  1  1  1  X  1  0  1  1  1  1 X^2  1  0  1  1  1 X^2+X  0  1 X^2+X X^2  1  1  1 X^2+X  1  1  X X^2  1  1  1 X^2  1  1  1  1 X^2 X^2+X X^2  1  1  1  1  1  1  1  X  1  1  1  1  1  X X^2 X^2  1  1  1  1  1  0
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  X X^2+X+1  1  1 X^2+1  0  1  1  0  1 X+1 X^2+X X^2+1 X^2  1 X+1  1 X+1  0 X^2+X  1  1 X+1  1  1 X^2+1 X^2+1 X^2+X  1 X^2+1 X^2+X+1  1  1 X^2+1 X+1 X+1  1  0  1 X^2+X+1  X  1  1  1  0 X^2+X X^2+X+1 X^2+X+1 X^2 X^2+X+1 X^2+1  1  0 X^2+X  1 X^2 X+1 X^2+X  1  1  0 X^2 X^2+X+1  0 X^2  X
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 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+214x^76+252x^78+724x^80+508x^82+754x^84+532x^86+634x^88+244x^90+202x^92+13x^96+8x^100+2x^104+4x^108+2x^112+2x^116

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 2.24 seconds.