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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+54x^66+210x^67+495x^68+204x^69+57x^70+2x^71+1x^130

The gray image is a code over GF(2) with n=544, k=10 and d=264.
This code was found by Heurico 1.16 in 6.13 seconds.