The generator matrix

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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+192x^70+706x^71+498x^72+694x^73+472x^74+490x^75+270x^76+290x^77+121x^78+184x^79+44x^80+40x^81+62x^82+28x^83+2x^84+1x^86+1x^96

The gray image is a code over GF(2) with n=592, k=12 and d=280.
This code was found by Heurico 1.16 in 0.313 seconds.