The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2  2  1  1  1  1  1  2  1 X+2  1  1  1  1 X^2+X+2  1  1 X+2  1  1 X^2+2 X^2 X+2  1 X^2+X+2 X^2+X  1  1  1  1  1  1  1  0  X  1  1 X^2+X  0  1  2  1 X^2+X+2  1  1  X  1  1  1  1 X^2+X
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+X X+1  X X+1 X^2+2  1  1  1 X^2  2 X^2+1  3  1 X^2+X+3 X+2  1 X^2+1 X^2+X+2  X  1  1 X^2+1  1  1 X^2+X+3 X^2+X+3  1 X+3 X+1 X+2  2  1  X X^2+X X^2+1  1  1 X+3  1 X^2+X  1 X^2+X+1  0 X^2+X X^2+2 X+1 X^2+X+2  X  1
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X+2 X^2+X X^2 X^2 X^2+X X^2+X X^2+2 X^2 X^2+X+2 X^2 X+2  2  X X^2+2 X^2+2 X^2+X  X X^2+X X^2 X+2 X^2+2 X^2+X  X X+2  0 X^2+X  0 X^2+X X+2 X^2  0  2  2 X+2 X+2  0 X^2+2 X^2 X^2+X X^2+X+2 X^2+X  X  2  X X^2+X+2  0 X^2+X+2 X^2  2 X^2+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  2  0  2  2  0  2  2  2  2  0  0  2  0  0  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 64.

Homogenous weight enumerator: w(x)=1x^0+325x^64+500x^65+603x^66+428x^67+578x^68+544x^69+410x^70+296x^71+196x^72+72x^73+73x^74+4x^75+25x^76+12x^77+18x^78+8x^80+1x^84+2x^88

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 0.5 seconds.