The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  0  1  1 X+2  1  1  2  1  1  X  1  1  0  1  1 X+2  1  1  1  1  2  X  1  1  X  X  0  X  2  X  1  1  0  2  1  1  1  1 X+2  X  X  X  X  X  0  2  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  2 X+3  X  1  1  1  0 X+2  0 X+2  X  X  X  2 X+1 X+3  1  1  2  X  3  1  1  1  0  2 X+2  X  X  X  0  2 X+1 X+3 X+2  X  0  2

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

Homogenous weight enumerator: w(x)=1x^0+49x^68+4x^70+4x^72+4x^74+1x^76+1x^80

The gray image is a code over GF(2) with n=272, k=6 and d=136.
This code was found by Heurico 1.16 in 0.0887 seconds.