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  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^2  1  1  1  X  1  X  1  1 X^3+X^2  1  1  X  X  0  0 X^2 X^2
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^2 X^2+X  0 X^3 X^3+X X^3+X  0 X^2 X^3+X X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3+X^2 X^2+X X^3+X^2  X  0 X^2  X  X X^3+X^2 X^3+X X^3 X^3+X X^2 X^3+X X^3+X^2 X^3+X^2 X^2+X  0 X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2 X^3+X^2+X X^2+X X^2 X^3 X^3 X^2+X  X X^2  0 X^2+X  X X^3+X X^2+X X^3+X^2 X^3  X X^3+X^2+X  X X^2  0  0  0 X^3+X^2 X^2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3+X^2  0 X^3+X X^2+X X^3  0 X^3+X^2+X X^2+X X^3+X^2 X^3+X^2 X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X X^3 X^3 X^3+X X^3+X  0 X^3 X^3+X X^3+X X^3 X^2+X X^2 X^3+X^2 X^3+X^2+X  X X^3 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X X^2+X X^3 X^2 X^3 X^3+X X^2 X^3 X^2+X X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^3+X  0 X^3+X^2 X^2 X^3 X^3+X^2+X X^3+X  0  0 X^2 X^3+X^2+X X^2+X  X  X  X  X
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3  0  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+216x^70+48x^71+342x^72+336x^73+240x^74+336x^75+271x^76+48x^77+152x^78+24x^80+32x^82+1x^92+1x^128

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 0.468 seconds.