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  1  X  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
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  0  2  0  2  2  2  0  2  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  2  0  2  2  2  0  2  2  0  2  2  2  0  2  2  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  0  2  0  2  0  2  0  2  2  2  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  0  2  2  2  0  2  2  2  2  2  2  0  2  2  2  2
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  2  2  0  0  0  0  0  0  2  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  0  0  2  0  2  2  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  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  2  0  2  2  2  2  0  2  2  0  2  2  0  2  2  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  0  2  0  0  0  0  2  2  0  0  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  0  2  0  2  0  0  0  0  0  0  0  2  0  2  0

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+38x^64+96x^66+256x^67+80x^68+32x^70+8x^72+1x^128

The gray image is a code over GF(2) with n=268, k=9 and d=128.
This code was found by Heurico 1.16 in 90.5 seconds.