The generator matrix

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

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+32x^60+16x^61+55x^62+144x^63+63x^64+784x^65+32x^66+784x^67+8x^68+8x^70+16x^71+16x^72+16x^73+16x^74+16x^75+8x^76+16x^77+16x^78+1x^126

The gray image is a code over GF(2) with n=528, k=11 and d=240.
This code was found by Heurico 1.16 in 0.375 seconds.