The generator matrix

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

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+76x^63+202x^64+228x^65+366x^66+478x^67+472x^68+538x^69+460x^70+446x^71+345x^72+200x^73+176x^74+46x^75+11x^76+18x^77+4x^78+8x^79+7x^80+8x^81+2x^82+2x^87+1x^92+1x^104

The gray image is a code over GF(2) with n=552, k=12 and d=252.
This code was found by Heurico 1.16 in 0.797 seconds.