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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+26x^70+62x^71+63x^72+54x^73+92x^74+422x^75+667x^76+370x^77+111x^78+70x^79+24x^80+18x^81+22x^82+18x^83+13x^84+6x^85+2x^86+4x^87+2x^90+1x^142

The gray image is a linear code over GF(2) with n=608, k=11 and d=280.
This code was found by Heurico 1.16 in 0.562 seconds.