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

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

Homogenous weight enumerator: w(x)=1x^0+17x^66+206x^68+576x^69+206x^70+16x^72+1x^74+1x^136

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 0.313 seconds.