The generator matrix

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

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+320x^64+80x^66+280x^68+32x^70+268x^72+16x^74+24x^76+2x^80+1x^128

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 2.61 seconds.