The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^69+164x^70+284x^71+413x^72+364x^73+307x^74+172x^75+58x^76+48x^77+64x^78+56x^79+16x^80+8x^81+1x^138

The gray image is a code over GF(2) with n=584, k=11 and d=276.
This code was found by Heurico 1.16 in 14.3 seconds.