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

generates a code of length 67 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+26x^65+206x^66+556x^67+207x^68+26x^69+1x^70+1x^130

The gray image is a code over GF(2) with n=536, k=10 and d=260.
This code was found by Heurico 1.16 in 8.95 seconds.