The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  0  1  1  1  1  1  2  1  2
 0  X  0 X+2  0 X+2  0  X  0 X+2 X+2  0  X  0  0  X  0 X+2  0  X  0 X+2  X  2  2 X+2  2 X+2  0 X+2  2 X+2  0 X+2 X+2  2  0 X+2  X  2  X  X  0  2  2 X+2 X+2  2  0  X  X  2  2  0  X  0  2 X+2  0  2  0  2 X+2 X+2 X+2  2 X+2  2
 0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  0  2  2  2  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  2  0
 0  0  0  2  0  0  0  2  0  0  2  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  0  0  0  2  2  2  2  0  2  2  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  0  2  0  2  2  2  2  2  0  2  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  0  0  0  0  0
 0  0  0  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  2  0  0  0  0  0  0  0  2  0  0  2  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  0  0  2  2  2  0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  0  2  0  2  2  0  2  2  0  0  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+302x^64+256x^66+64x^68+256x^70+32x^72+64x^76+48x^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 0.281 seconds.