The generator matrix

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

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+407x^60+1150x^61+2196x^62+2984x^63+3547x^64+4318x^65+4393x^66+4016x^67+3426x^68+2622x^69+1672x^70+1040x^71+596x^72+202x^73+110x^74+24x^75+23x^76+28x^77+12x^78+1x^82

The gray image is a code over GF(2) with n=528, k=15 and d=240.
This code was found by Heurico 1.16 in 11 seconds.