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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+3x^68+24x^69+3x^70+1x^74

The gray image is a code over GF(2) with n=268, k=5 and d=136.
This code was found by Heurico 1.16 in 0.126 seconds.