The generator matrix

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

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+31x^66+250x^67+62x^68+334x^69+31x^70+310x^71+1x^72+2x^73+1x^98+1x^102

The gray image is a code over GF(2) with n=552, k=10 and d=264.
This code was found by Heurico 1.16 in 0.204 seconds.