The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+130x^60+998x^61+2599x^62+4438x^63+7601x^64+10014x^65+14477x^66+15878x^67+18533x^68+16140x^69+14965x^70+10658x^71+6983x^72+3766x^73+2263x^74+860x^75+457x^76+178x^77+56x^78+36x^79+23x^80+8x^81+4x^82+2x^83+4x^86

The gray image is a code over GF(2) with n=544, k=17 and d=240.
This code was found by Heurico 1.16 in 141 seconds.