The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+139x^62+908x^63+2357x^64+5126x^65+9295x^66+13896x^67+20890x^68+27284x^69+33124x^70+35062x^71+33785x^72+28564x^73+21304x^74+13588x^75+8611x^76+4394x^77+2123x^78+1030x^79+381x^80+154x^81+53x^82+24x^83+19x^84+14x^85+10x^86+4x^87+4x^88

The gray image is a code over GF(2) with n=568, k=18 and d=248.
This code was found by Heurico 1.16 in 684 seconds.