The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+104x^76+96x^78+37x^80+6x^84+1x^88+10x^92+1x^104

The gray image is a linear code over GF(2) with n=312, k=8 and d=152.
This code was found by Heurico 1.16 in 0.312 seconds.