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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+8x^65+9x^66+46x^67+406x^68+8x^69+22x^70+9x^72+1x^74+2x^99

The gray image is a code over GF(2) with n=544, k=9 and d=260.
This code was found by Heurico 1.16 in 0.297 seconds.