The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+156x^69+673x^70+892x^71+1138x^72+1220x^73+1046x^74+824x^75+638x^76+424x^77+407x^78+320x^79+232x^80+104x^81+81x^82+28x^83+5x^84+1x^88+1x^90+1x^92

The gray image is a code over GF(2) with n=592, k=13 and d=276.
This code was found by Heurico 1.16 in 1 seconds.