The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+192x^63+1153x^64+2826x^65+5097x^66+8080x^67+9681x^68+14188x^69+15614x^70+17448x^71+15519x^72+14422x^73+10722x^74+7668x^75+4026x^76+2406x^77+1192x^78+476x^79+194x^80+106x^81+29x^82+22x^83+1x^84+2x^85+2x^86+1x^88+2x^89+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 156 seconds.