The generator matrix

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

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+121x^66+594x^67+1451x^68+2032x^69+2926x^70+3776x^71+3520x^72+4348x^73+3812x^74+3364x^75+2781x^76+1956x^77+965x^78+504x^79+239x^80+160x^81+126x^82+16x^83+42x^84+16x^85+9x^86+6x^88+1x^90+2x^91

The gray image is a code over GF(2) with n=584, k=15 and d=264.
This code was found by Heurico 1.16 in 12.3 seconds.