The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+370x^60+1322x^61+1929x^62+3334x^63+3108x^64+4710x^65+3849x^66+4574x^67+3064x^68+2996x^69+1569x^70+1006x^71+445x^72+286x^73+91x^74+58x^75+24x^76+14x^77+10x^78+4x^79+4x^80

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 10.7 seconds.