The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+76x^63+574x^64+868x^65+1309x^66+1184x^67+1212x^68+736x^69+678x^70+528x^71+391x^72+232x^73+245x^74+52x^75+60x^76+36x^77+8x^78+2x^84

The gray image is a code over GF(2) with n=544, k=13 and d=252.
This code was found by Heurico 1.16 in 0.797 seconds.