The generator matrix

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

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+304x^65+375x^66+308x^67+267x^68+328x^69+175x^70+148x^71+19x^72+28x^73+57x^74+24x^75+4x^77+8x^81+1x^92+1x^94

The gray image is a code over GF(2) with n=544, k=11 and d=260.
This code was found by Heurico 1.16 in 65.1 seconds.