The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  0  2  1  1  1  1  0  1  1  1  1  0  2  0  0  X X+2  X X+2 X+2  X X+2  X  X  1  1  1  1 X+2  1  1  1  1  1 X+2  1  1  1  1  2  1  1  1  1  1  1  1 X+2  1  2  1  1  1
 0  1  0  0  3  3  1 X+2  1  1  X X+3  X X+3  2  1  0 X+3  0 X+3  1  X  3  X  3  1  1  2  X  1  1  1  1  1  1  1  1  X  1 X+3 X+3  1  2  0 X+2 X+3  1 X+3 X+2  1  2  X  3  X  0 X+2 X+1  3 X+1  X  2  0 X+3  X X+1 X+1 X+3
 0  0  1 X+1 X+3  2 X+3  1 X+2  1  X X+2  1  3  1 X+1 X+2 X+1  3  0  2  2  X X+3  1 X+2  1  1  1  X  3  2 X+1 X+2  1  2 X+1  1  1 X+1  2 X+2  1  2 X+2  X X+1  1  1  X X+2  2  2  1 X+3  3  2 X+3 X+3 X+3  3  1  0  0 X+2  X  X
 0  0  0  2  2  0  2  2  2  0  2  2  0  0  2  0  0  0  2  2  2  2  0  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  0  2  0  2  0  2  0  0  0  2  0  2  2  0  2  0  0  2  0  0  2  2  0  0  0  2  2  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+419x^64+216x^66+156x^68+16x^70+136x^72+56x^74+12x^76+12x^80

The gray image is a code over GF(2) with n=268, k=10 and d=128.
This code was found by Heurico 1.16 in 46.5 seconds.