The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1 3X  1  1  1  1  0  1 3X+2  1  1  1  2  1 3X  1  1  1  0  1  1 3X+2  1  2  1  1 3X  1  1  1  1  1  1  1  1  1  X  1  1  0  1  1 3X+2  0  1  X  X  1  1 2X  1  1  1 3X+2  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 2X+1  1 3X 3X+2  0 X+1  1 2X+3  1  2 3X X+3  1 2X+1  1 3X+2  0 X+1  1  2 2X+1  1 3X  1 X+3 2X+3  1 3X+2  0 2X 3X  2 3X+2  2 X+2 2X+2  0 3X X+1  1  X 3X+1  1  X  X 3X+2 X+2 3X  2  1 2X+1 2X+1  2  1  0 2X  0
 0  0 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X  0  0  0 2X  0 2X  0  0  0 2X  0
 0  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X  0  0  0 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0  0  0  0  0  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0  0  0  0  0  0  0  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+9x^60+164x^61+232x^62+444x^63+360x^64+648x^65+390x^66+744x^67+308x^68+420x^69+196x^70+92x^71+22x^72+48x^73+8x^74+1x^76+4x^78+2x^82+2x^92+1x^96

The gray image is a code over GF(2) with n=528, k=12 and d=240.
This code was found by Heurico 1.16 in 0.375 seconds.