The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+72x^60+596x^61+1088x^62+1702x^63+1844x^64+2174x^65+2068x^66+2066x^67+1624x^68+1348x^69+799x^70+436x^71+239x^72+178x^73+59x^74+62x^75+2x^76+8x^77+7x^78+6x^79+2x^80+1x^82+2x^86

The gray image is a code over GF(2) with n=528, k=14 and d=240.
This code was found by Heurico 1.16 in 2.95 seconds.