The generator matrix

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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+252x^70+52x^71+270x^72+56x^73+770x^74+128x^75+228x^76+8x^77+256x^78+12x^79+12x^80+1x^82+1x^96+1x^114

The gray image is a linear code over GF(2) with n=592, k=11 and d=280.
This code was found by Heurico 1.16 in 0.312 seconds.