The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+224x^66+1472x^67+2783x^68+4094x^69+5242x^70+7396x^71+7700x^72+8692x^73+7489x^74+6882x^75+5225x^76+3820x^77+2156x^78+1364x^79+543x^80+268x^81+85x^82+50x^83+34x^84+6x^85+4x^87+2x^88+4x^90

The gray image is a code over GF(2) with n=584, k=16 and d=264.
This code was found by Heurico 1.16 in 39.9 seconds.