The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+320x^65+474x^66+708x^67+522x^68+498x^69+398x^70+424x^71+271x^72+212x^73+77x^74+76x^75+29x^76+58x^77+9x^78+8x^79+8x^80+1x^82+1x^84+1x^86

The gray image is a code over GF(2) with n=552, k=12 and d=260.
This code was found by Heurico 1.16 in 0.515 seconds.