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  0  X X^3+X^2  X  0  X X^3+X^2  X  0  X X^3+X^2  X  X  X  0  X X^2  X  X  X  X  X  X  X  X  X  X  X  X  X  1  X  X  1 X^3  1  1 X^3  X  X  1  1  X
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2  X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^2+X  X X^3+X  X  0 X^3+X^2 X^2+X  X X^3+X  X  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X X^3+X^2+X  X X^3+X  X  0 X^3+X  X X^3+X^2+X  X X^3+X^2 X^2+X  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+157x^74+205x^76+133x^78+9x^80+1x^82+1x^84+1x^86+2x^90+2x^94

The gray image is a linear code over GF(2) with n=608, k=9 and d=296.
This code was found by Heurico 1.16 in 9.92 seconds.