The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+498x^63+1192x^64+2288x^65+2795x^66+3930x^67+3814x^68+4464x^69+3764x^70+3458x^71+2646x^72+2080x^73+854x^74+488x^75+219x^76+134x^77+57x^78+40x^79+15x^80+20x^81+1x^82+2x^83+1x^84+6x^85+1x^86

The gray image is a code over GF(2) with n=552, k=15 and d=252.
This code was found by Heurico 1.16 in 96.2 seconds.