The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^62+912x^63+2321x^64+5122x^65+9121x^66+14404x^67+21175x^68+27500x^69+32526x^70+34038x^71+34279x^72+28724x^73+21100x^74+14352x^75+8401x^76+4392x^77+2106x^78+932x^79+353x^80+142x^81+75x^82+28x^83+26x^84+4x^85+4x^86+6x^87+2x^88+4x^89+2x^92

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 634 seconds.