The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+234x^66+500x^67+314x^68+172x^69+236x^70+356x^71+81x^72+36x^73+72x^74+24x^75+12x^76+8x^82+2x^98

The gray image is a code over GF(2) with n=552, k=11 and d=264.
This code was found by Heurico 1.16 in 0.25 seconds.