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

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+91x^60+139x^64+256x^65+1152x^66+256x^67+88x^68+8x^72+44x^76+12x^80+1x^124

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 107 seconds.