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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+28x^76+3x^80

The gray image is a linear code over GF(2) with n=296, k=5 and d=152.
This code was found by Heurico 1.16 in 0.186 seconds.