The generator matrix

 1  0  0  0  1  1  1  1 2X  1  1  1 2X+2 3X+2 X+2  1  1  1  X  1 X+2  1 X+2 2X  1 3X+2 3X 3X  1  1  1 X+2 3X+2  1  2 2X 3X  1  1  1  1  1  1  1  1  X 2X X+2  1  1  1 3X X+2  X  1 3X 2X+2  1 2X+2  1 2X  1  1 3X  X  1
 0  1  0  0  X 2X+3 3X+2 X+3  1 3X  1 3X+3  1  1 2X+2 X+2  2  2  1  3 X+2 X+3  1  1 3X+3  2  1  2 X+1 2X+2 3X  1 3X+2 2X+2  1  1 3X+2  2 2X+3 3X+2 3X 3X+3  3  1 2X+2  1  1  1 2X+2 X+1 3X+2  0 2X+2 2X 3X  1  1 X+1  1 3X+3  1  X 3X  X  1  0
 0  0  1  0  0 2X 3X+1 X+1 X+3  1  3 2X+2 2X+3  0  1 3X X+3 2X+1 3X+3 2X+2  1  3 3X+2 3X+2  1  1 2X+1 3X+2 2X+2 3X+2  3 2X+2 3X+2  X  0 2X  1 2X+1 X+1 3X+3 X+1 3X+2 3X 3X+1  0 3X+1  1 3X+1 3X X+1  2 3X+2  1  0 X+3 2X+1 X+1 3X+2 3X+2  2  3  1 2X  1 2X+2  0
 0  0  0  1  1 3X+1 3X+3  3  X X+2  2 2X  1 2X+1 X+3 X+2 3X X+1 3X+1  1  X  X 3X+2 X+3 3X+1  3 3X+2  1  X 2X+3  0 X+2  1 3X+3 X+2 X+1 2X+1 2X+2 2X+1 X+1  3 3X 3X  0 2X+3 2X+1 X+2  2 X+2  2  0  1 2X  1  0 2X+2  2 X+1 2X+1 X+3 2X  1 2X+1 3X  0  0
 0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0  0  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  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 58.

Homogenous weight enumerator: w(x)=1x^0+125x^58+966x^59+2716x^60+4500x^61+7129x^62+10674x^63+13414x^64+17224x^65+17338x^66+17762x^67+14000x^68+10380x^69+6832x^70+4010x^71+2234x^72+1096x^73+385x^74+184x^75+62x^76+16x^77+13x^78+4x^79+3x^80+2x^84+2x^86

The gray image is a code over GF(2) with n=528, k=17 and d=232.
This code was found by Heurico 1.16 in 141 seconds.