The generator matrix

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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+160x^63+1096x^64+2688x^65+4912x^66+7484x^67+10600x^68+13592x^69+16752x^70+16700x^71+16290x^72+14386x^73+11098x^74+7018x^75+4206x^76+2250x^77+1030x^78+396x^79+257x^80+70x^81+46x^82+16x^83+14x^84+6x^85+2x^86+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 159 seconds.