The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+68x^63+213x^64+628x^65+501x^66+496x^67+440x^68+506x^69+431x^70+440x^71+148x^72+144x^73+40x^74+18x^75+7x^76+2x^77+1x^78+4x^80+2x^82+2x^83+2x^88+1x^90+1x^92

The gray image is a code over GF(2) with n=544, k=12 and d=252.
This code was found by Heurico 1.16 in 0.437 seconds.