The generator matrix

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

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+90x^63+673x^64+1214x^65+1582x^66+1954x^67+1847x^68+2360x^69+1615x^70+1664x^71+1278x^72+988x^73+631x^74+232x^75+143x^76+60x^77+16x^78+10x^79+16x^80+2x^81+2x^82+2x^83+1x^86+2x^88+1x^90

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 3.12 seconds.