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 X^2  1  1  1  1  1  0  1  1  1  1  X  1  X  1  1  1  1  1  X  1  1  1  X  1  X  1  0  1 X^2 X^3  1  X  1  X  1  1  X  X  1 X^2 X^2 X^2  1  X X^3  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^2+X X^3+X^2 X^3+X^2+X X^3+X X^3+X^2 X^2 X^3+X X^3+X^2 X^3+X  0 X^3 X^2+X X^2 X^2+X X^2  0  X X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X X^3+X^2+X  0  X X^3 X^2  0 X^2+X  X X^3+X^2 X^2+X X^3+X^2 X^3+X X^2+X X^3+X^2+X X^3+X X^2+X  X X^3+X^2 X^3+X^2  X  X X^3+X X^3 X^2+X X^3+X X^3+X^2 X^2+X  0 X^3+X^2+X X^3+X^2  X  X X^3+X^2+X X^3+X X^2 X^3  0
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  0 X^3  X  0 X^3+X X^2  0 X^3 X^2+X X^2+X  X X^2 X^3+X^2 X^3+X X^3+X^2+X  X  X X^2 X^3+X^2  0  X X^3+X^2 X^2 X^2+X X^3+X^2+X  0 X^3 X^2+X X^3+X^2  X X^2+X  X  X X^3+X^2  X X^3+X^2 X^2+X X^2  0  X X^3+X^2  0  X  X X^3 X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3  X X^3  0 X^3  0  X  X  0
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2  0 X^2  0  0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2  0 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  0 X^3  0 X^3+X^2 X^3 X^3+X^2 X^2 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0  0  0 X^3+X^2  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+21x^70+240x^71+315x^72+326x^73+599x^74+320x^75+705x^76+312x^77+452x^78+244x^79+233x^80+130x^81+55x^82+40x^83+33x^84+36x^85+11x^86+4x^87+1x^88+12x^89+5x^90+1x^114

The gray image is a linear code over GF(2) with n=608, k=12 and d=280.
This code was found by Heurico 1.16 in 0.766 seconds.