The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^63+653x^64+1172x^65+1518x^66+1930x^67+1989x^68+2330x^69+2187x^70+1504x^71+1061x^72+796x^73+568x^74+322x^75+165x^76+70x^77+28x^78+12x^79+17x^80+2x^82+4x^83+2x^84+1x^86

The gray image is a code over GF(2) with n=552, k=14 and d=252.
This code was found by Heurico 1.16 in 3.14 seconds.