The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  2  1  X  1  1  1  1  2  X  1  1  1  1  1  1  1  1  2  X  2  X  X  X  X  0  X  X  X  0  0  1  1  1  1  X  X  2  X  X  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  2  X X+3  1  1  1  2  X X+3  1  1  1  2  X  2  X X+3  1 X+3  1  1  1  1  1  0 X+2  0  X  0 X+2 X+2  X  X  0  2  0  2  X  2  X X+2  X  3
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  0  0  2  2  0  0  0  2  2  2  2  0  2  0  2  0  2  0  2  2  0  0  0  2  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  0  2  0  0  2  2  2  0  2  0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  2  0  2  2  2  0  2  0  0  0  2  2  0  0  0  0  2  0

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+92x^65+17x^66+32x^67+30x^68+58x^69+14x^70+1x^72+8x^73+1x^74+2x^77

The gray image is a code over GF(2) with n=268, k=8 and d=130.
This code was found by Heurico 1.16 in 0.146 seconds.