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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  0  2  2  2  0  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  2  0  0  2  2  2  2  0  0  2  0  2  2  2  2  0  0  0  0  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  2  2  2  0  0  2  0  2  2  2  0  0  0  0  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  0  0  2  2  2  0  0  0  0  0
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  0  2  2  0  2  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  2  0  2  0  0  0  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+31x^64+190x^68+32x^72+2x^100

The gray image is a code over GF(2) with n=272, k=8 and d=128.
This code was found by Heurico 1.16 in 0.143 seconds.