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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+3x^76+24x^77+3x^78+1x^90

The gray image is a linear code over GF(2) with n=300, k=5 and d=152.
This code was found by Heurico 1.16 in 0.215 seconds.