The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^70+654x^71+700x^72+762x^73+418x^74+368x^75+273x^76+314x^77+137x^78+146x^79+88x^80+72x^81+29x^82+20x^83+2x^88+2x^90

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.