The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+236x^64+184x^66+264x^68+152x^70+106x^72+48x^74+24x^76+3x^80+5x^88+1x^104

The gray image is a code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 3.92 seconds.