The generator matrix

 1  0  1  1  1 3X+2  1  X  1 2X  1  1  2  1  1  1 X+2  1  1 2X+2  1 3X  1  1  1  1  1 3X  1  0  1  1  1  1  1 2X 3X+2  1  1 X+2 2X+2  1  1  1  2 X+2  1  1  X 2X  1  1  1  1  1  1  X 2X  1  1 2X+2  0  1  X 3X  X  1  X
 0  1 X+1 X+2 2X+3  1 2X+2  1 X+3  1 3X  1  1 2X X+1 3X+2  1 3X+3  2  1  X  1 X+1 3X+3  3 2X+1  0  1  3  1 3X+2 3X+1  2 2X+3 X+2  1  1 2X+1 3X+1  1  1 X+2 2X+2 3X  1  1 2X  1 2X+2  X  1 2X+3 X+3  X 3X+3  0  0  1 2X+2  2  1  1  X  0  1 2X+2 3X+2 3X+2
 0  0  2  0 2X+2  2  0  2 2X+2 2X+2  0  2 2X+2  2 2X 2X+2  0 2X  2  0 2X+2  0 2X 2X  0 2X  0  0 2X  0 2X+2  2  2 2X+2 2X  2  2  0  2  2 2X  2  0 2X  2 2X 2X+2 2X+2  2  0  0 2X  2 2X  2  2 2X 2X  2 2X+2  2 2X+2  0 2X+2  0  0 2X+2 2X+2
 0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0  0  0  0 2X  0 2X  0  0 2X 2X  0 2X 2X 2X  0  0
 0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0 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+106x^63+305x^64+434x^65+487x^66+558x^67+502x^68+466x^69+475x^70+356x^71+204x^72+84x^73+61x^74+20x^75+8x^76+4x^77+1x^78+10x^79+2x^80+2x^81+6x^83+2x^84+2x^85

The gray image is a code over GF(2) with n=544, k=12 and d=252.
This code was found by Heurico 1.16 in 0.641 seconds.