The generator matrix

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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+144x^57+770x^58+2100x^59+4932x^60+8268x^61+14542x^62+20112x^63+28311x^64+32700x^65+37078x^66+33684x^67+29646x^68+20456x^69+13926x^70+7788x^71+4304x^72+1916x^73+930x^74+280x^75+158x^76+36x^77+40x^78+4x^79+4x^80+10x^82+4x^84

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 578 seconds.