The generator matrix

 1  0  0  1  1  1 X^3  1  1  0  1  1 X^2 X^3+X^2+X  1 X^3+X X^3+X  X  1  1  1  1 X^3+X X^2+X  1  1 X^3  1  1  1  1 X^3+X^2  1  1  1  X  X  1  1 X^3+X X^3+X^2  1 X^3+X^2  1  1 X^3+X  X  1  0  X X^3+X^2  1  0  1  1  1  1  1  1  1  1  1  X X^3+X^2  1  1 X^3+X^2+X X^3+X^2+X X^3+X^2+X  1  1  1  1  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X  X X^3+X^2+X+1 X^2+X+1  1  1 X^2  1  0  1 X^3+X^2+X X^3+X^2+1 X^3+1 X^3  X  1 X^2 X^3+X+1  1 X^2+X X^3+X^2 X^3+X  1  1 X^3+X^2+1 X^3+X^2+X X+1  1  1 X^2+X+1 X^3+X^2+X+1  1  1 X^3+X+1 X^3 X^2+1  X  1 X^2 X^3+X+1 X^2+X  1  1 X^2+1  1 X^3+X^2 X+1  1 X^3+X^2+X+1 X^2+X  X X^2 X^3 X^3+X+1 X^3+X^2  1  0 X^3+X^2+X  X X^2+X  0 X^3+1 X^3+1 X^3+X^2+X+1 X^2+X  0
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1 X^3+X^2+1 X^2+X  X X^3+1 X^3+X  X  1 X+1 X^3+X+1 X^2+X X^3+X^2+1  1  1 X^2+X X^3+X^2 X^2+X+1 X^3+1  1 X^3+X^2+X X+1 X^3+X^2+X+1 X^2+X  X X^3+X^2+X  X X^2+X+1  1 X+1 X^2 X^2  1 X^2+1  1 X^2  0 X^3  1  0  1 X^2+X X^3+X^2 X^3+1 X^2+X+1 X^3 X^3+X^2+X X^3+X^2  0 X^3+X^2+X+1 X^2 X^3+X+1 X^2+1 X^3+1  0 X^3 X^2+X+1 X^2  1  1  1 X^3+X  0  X X^3+X^2+X  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+134x^70+628x^71+720x^72+676x^73+459x^74+508x^75+262x^76+204x^77+140x^78+108x^79+83x^80+104x^81+34x^82+12x^83+16x^84+6x^88+1x^90

The gray image is a linear code over GF(2) with n=592, k=12 and d=280.
This code was found by Heurico 1.16 in 0.328 seconds.