The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+88x^57+828x^58+2038x^59+4822x^60+8826x^61+14150x^62+20494x^63+27299x^64+34230x^65+35656x^66+34434x^67+28555x^68+21306x^69+14083x^70+7828x^71+4208x^72+1926x^73+764x^74+352x^75+165x^76+36x^77+21x^78+18x^79+6x^80+4x^81+2x^82+4x^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 565 seconds.