The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^69+611x^70+1032x^71+1227x^72+1066x^73+1044x^74+796x^75+778x^76+404x^77+473x^78+288x^79+152x^80+122x^81+34x^82+28x^83+25x^84+8x^85+6x^86+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 0.937 seconds.