The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^62+654x^63+885x^64+2030x^65+1522x^66+2584x^67+1713x^68+2376x^69+1324x^70+1402x^71+659x^72+682x^73+185x^74+196x^75+47x^76+46x^77+3x^78+12x^79+7x^80+1x^82+2x^85+3x^86

The gray image is a code over GF(2) with n=544, k=14 and d=248.
This code was found by Heurico 1.16 in 3.05 seconds.