The generator matrix

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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+142x^64+566x^65+776x^66+562x^67+562x^68+484x^69+300x^70+230x^71+161x^72+82x^73+97x^74+76x^75+29x^76+16x^77+9x^78+1x^80+2x^82

The gray image is a code over GF(2) with n=544, k=12 and d=256.
This code was found by Heurico 1.16 in 0.265 seconds.