The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+198x^62+1296x^63+2498x^64+4108x^65+5555x^66+7158x^67+7480x^68+9152x^69+8005x^70+7256x^71+4990x^72+3642x^73+2185x^74+1102x^75+520x^76+268x^77+37x^78+52x^79+15x^80+14x^81+4x^82

The gray image is a code over GF(2) with n=552, k=16 and d=248.
This code was found by Heurico 1.16 in 38.5 seconds.