The generator matrix

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

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+486x^61+1216x^62+2126x^63+2804x^64+3892x^65+3849x^66+4566x^67+3853x^68+3738x^69+2498x^70+1770x^71+1000x^72+556x^73+202x^74+100x^75+45x^76+28x^77+14x^78+12x^79+1x^80+4x^81+5x^82+2x^83

The gray image is a code over GF(2) with n=536, k=15 and d=244.
This code was found by Heurico 1.16 in 11.3 seconds.