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

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

Homogenous weight enumerator: w(x)=1x^0+134x^74+48x^76+29x^78+15x^80+17x^82+11x^86+1x^90

The gray image is a linear code over GF(2) with n=304, k=8 and d=148.
This code was found by Heurico 1.16 in 17.4 seconds.