The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+244x^65+198x^66+176x^67+172x^68+196x^69+10x^70+24x^71+1x^76+1x^88+1x^100

The gray image is a code over GF(2) with n=536, k=10 and d=260.
This code was found by Heurico 1.16 in 0.906 seconds.