The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+104x^59+788x^60+2382x^61+4779x^62+8670x^63+13853x^64+20446x^65+27058x^66+33764x^67+36454x^68+35168x^69+28442x^70+21236x^71+13476x^72+7988x^73+4110x^74+2020x^75+914x^76+242x^77+143x^78+58x^79+18x^80+10x^81+12x^82+4x^87+4x^89

The gray image is a code over GF(2) with n=544, k=18 and d=236.
This code was found by Heurico 1.16 in 588 seconds.