The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^68+1x^72

The gray image is a code over GF(2) with n=264, k=5 and d=136.
This code was found by Heurico 1.16 in 0.12 seconds.