The generator matrix

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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+154x^59+1212x^60+2426x^61+3972x^62+5110x^63+7655x^64+7778x^65+9167x^66+8040x^67+7637x^68+5120x^69+3482x^70+1848x^71+1140x^72+426x^73+235x^74+62x^75+49x^76+10x^77+8x^78+2x^79+2x^80

The gray image is a code over GF(2) with n=528, k=16 and d=236.
This code was found by Heurico 1.16 in 37.5 seconds.