The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+162x^57+820x^58+2248x^59+4803x^60+8276x^61+13964x^62+20460x^63+28074x^64+33360x^65+36634x^66+33956x^67+29374x^68+20898x^69+13828x^70+7866x^71+3993x^72+1862x^73+907x^74+338x^75+181x^76+94x^77+22x^78+10x^79+6x^80+4x^81+1x^82+2x^83

The gray image is a code over GF(2) with n=528, k=18 and d=228.
This code was found by Heurico 1.16 in 583 seconds.