The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+172x^63+1223x^64+2732x^65+4677x^66+7362x^67+10559x^68+13864x^69+16455x^70+16830x^71+16923x^72+14144x^73+10439x^74+7154x^75+4521x^76+2202x^77+1009x^78+462x^79+211x^80+72x^81+28x^82+14x^83+10x^85+4x^87+2x^88+2x^91

The gray image is a code over GF(2) with n=568, k=17 and d=252.
This code was found by Heurico 1.16 in 155 seconds.