The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  2  1  1  X  X  1  1  1 X+2  1  1  1 X+2  1  0  1  0  1  1  1  1  1  0  1  X  0  1 X+2  1  1  1  2  1  0  X  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1  X  2  X  1  2
 0  1  1 X+2 X+1  1  3  2  1  2  1  1  X X+3  1  1  X  3 X+1  1  0 X+2  1  1 X+3  1 X+3  1  2  X X+3 X+2  1  1 X+2  1  1  0  1 X+3  0  1  X X+1  1  1  3  0 X+2  0  2 X+2  0  2  X  X  0  2  2 X+2 X+1  0 X+2  1  1 X+1  2
 0  0  X  0  2  0  2  X  X X+2 X+2 X+2  X  X  0  X X+2  0  0 X+2  2  2 X+2  2 X+2  2  X  0  2  2  0 X+2  0 X+2  X X+2  X X+2  X  2  X  2  2 X+2  2  2  X  0  0  2  2  2  2  X  2  X  X X+2  0  0 X+2 X+2  2  0 X+2  2  X
 0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  0  2  2  0  2  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  2  0  2  0  0  2  0  2  2  2  2  2  2  2  0  0  0  0  0  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+139x^64+128x^66+142x^68+60x^70+34x^72+4x^74+2x^88+2x^92

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 0.209 seconds.