The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+62x^61+543x^62+1130x^63+1695x^64+1810x^65+2261x^66+2174x^67+2031x^68+1456x^69+1331x^70+834x^71+532x^72+266x^73+122x^74+60x^75+43x^76+6x^77+12x^78+8x^79+2x^80+3x^82+2x^83

The gray image is a code over GF(2) with n=536, k=14 and d=244.
This code was found by Heurico 1.16 in 2.98 seconds.