The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+364x^69+451x^70+746x^71+416x^72+604x^73+281x^74+464x^75+244x^76+232x^77+118x^78+74x^79+8x^80+60x^81+12x^82+12x^83+2x^84+4x^85+1x^88+1x^90+1x^94

The gray image is a code over GF(2) with n=584, k=12 and d=276.
This code was found by Heurico 1.16 in 1 seconds.