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

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+7x^66+34x^67+175x^68+26x^69+8x^70+2x^71+2x^85+1x^102

The gray image is a code over GF(2) with n=544, k=8 and d=264.
This code was found by Heurico 1.16 in 0.219 seconds.