The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+94x^60+1034x^61+2378x^62+4814x^63+7121x^64+11000x^65+13196x^66+17388x^67+16679x^68+18140x^69+13638x^70+11014x^71+6550x^72+4162x^73+2093x^74+1122x^75+349x^76+144x^77+86x^78+28x^79+22x^80+14x^81+1x^82+2x^83+2x^85

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 151 seconds.