The generator matrix

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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+324x^73+347x^74+416x^75+132x^76+248x^77+231x^78+204x^79+43x^80+64x^81+12x^82+16x^83+4x^87+4x^89+1x^106+1x^110

The gray image is a linear code over GF(2) with n=608, k=11 and d=292.
This code was found by Heurico 1.16 in 0.328 seconds.