The generator matrix

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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+144x^62+766x^63+2469x^64+5588x^65+8337x^66+14610x^67+20774x^68+27870x^69+31860x^70+36276x^71+32472x^72+29272x^73+20792x^74+14472x^75+7994x^76+4750x^77+2166x^78+874x^79+406x^80+130x^81+55x^82+38x^83+8x^84+4x^85+6x^86+4x^87+2x^88+2x^89+2x^96

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 633 seconds.