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  1  1  1  1  X  1  1  1  1  0  1  X  1  1  X  X  1  2  1  1  X  1 2X  2  1  1  X  1  X  1 2X  1  2  X  X  1
 0  X  0  X 2X  0 X+2 3X+2  0 2X 3X  X 2X 3X+2 2X 3X+2 2X X+2 X+2  2 3X 2X+2 2X+2 X+2  X  2 2X+2  X 3X+2  0  X  0 2X+2  0 X+2  X 2X+2 2X 3X+2  X  2  X X+2 3X  2  X 3X+2 2X 2X+2  X 2X+2 3X 3X+2 3X+2  0 2X+2 X+2  2  X 2X 2X+2  X  X 3X+2 2X+2 3X+2  X 3X
 0  0  X  X  0 3X+2 X+2 2X  2 3X+2 3X+2  2 3X  2 2X+2  X 2X 2X X+2  X  2 X+2 2X X+2 X+2 3X  0  2 2X 2X 3X  X 2X X+2 3X 3X 3X  2  0  0  X 2X+2  X 3X 2X+2  2 2X+2 X+2  2 3X+2 2X+2 3X+2 3X+2 2X+2  X  X 2X+2  2  0  2 3X  X 2X  2  2  X  X 2X+2
 0  0  0  2  2 2X+2  0 2X+2  2 2X 2X+2  0  2 2X+2  0 2X 2X  0 2X  0  2 2X+2  2 2X+2  0 2X  0 2X+2 2X 2X+2 2X+2 2X+2 2X+2  0  2 2X 2X 2X  2 2X 2X+2 2X+2  0 2X+2  0 2X  0  2 2X+2  2  2  2  0  2 2X+2  2 2X 2X  2  0  0  0  0 2X 2X 2X  2  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+242x^63+269x^64+384x^65+325x^66+652x^67+630x^68+480x^69+358x^70+266x^71+147x^72+164x^73+28x^74+76x^75+24x^76+28x^77+8x^78+12x^79+1x^80+1x^106

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 54 seconds.