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

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+108x^70+108x^71+207x^72+632x^73+264x^74+312x^75+213x^76+32x^77+52x^78+36x^79+30x^80+24x^81+16x^82+8x^83+4x^84+1x^140

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 3.83 seconds.