The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+83x^62+580x^63+1152x^64+1582x^65+1883x^66+2252x^67+2076x^68+2046x^69+1499x^70+1270x^71+866x^72+560x^73+304x^74+112x^75+54x^76+30x^77+5x^78+10x^79+9x^80+6x^81+1x^82+2x^84+1x^86

The gray image is a code over GF(2) with n=544, k=14 and d=248.
This code was found by Heurico 1.16 in 2.99 seconds.