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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+6x^66+100x^67+6x^68+1x^70+12x^71+1x^72+1x^78

The gray image is a code over GF(2) with n=536, k=7 and d=264.
This code was found by Heurico 1.16 in 0.266 seconds.