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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+8x^75+5x^76+2x^78

The gray image is a linear code over GF(2) with n=284, k=4 and d=150.
This code was found by Heurico 1.16 in 0.158 seconds.