The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+38x^62+128x^63+355x^64+236x^65+555x^66+396x^67+744x^68+424x^69+475x^70+232x^71+300x^72+108x^73+75x^74+12x^75+6x^76+6x^78+1x^82+1x^86+2x^92+1x^106

The gray image is a code over GF(2) with n=544, k=12 and d=248.
This code was found by Heurico 1.16 in 0.406 seconds.