The generator matrix

 1  0  0  1  1  1  2 X^2+X+2  1  1  1  1 X^2+X X^2  1 X+2  1 X^2+2  X  1  1 X^2+X  1  1  1  X  0  1  2  1  1 X^2 X^2+X+2  1  1  X  2  1  1 X^2+2  1 X^2  1  1  1  1  0  2  2  1 X^2+X  X  1  X  1  1 X+2  1  1  1  1  1  1  1  1  1
 0  1  0  0 X^2+1 X^2+1  1  2  0 X^2  3  1  1  1 X+2  1 X+3 X^2+X+2  1 X^2+X+1 X^2+X+2 X+2 X+2 X^2+X+1 X+2  1  1 X+1  2 X^2+3 X^2  1  1 X^2+X+3 X^2+X+2 X+2  1 X^2 X^2+3  X X^2+2 X^2 X^2+X+2 X+3 X^2+X+2 X^2  1  1  1 X+2  1 X^2+2 X^2+X+1 X^2+X X+2 X^2+3  1 X^2+1 X+1  1 X^2+X X^2+X+1  3  3  X  0
 0  0  1 X+1 X^2+X+1  0 X+1  1 X^2+X+2  1  X  1 X^2  1 X^2+X  X  X  1 X^2+3 X^2  2  1 X^2+X+1 X^2+1 X^2+1 X+3 X^2+X+2 X^2+X+1  1 X+1  3 X^2+3 X^2+X+2 X^2+X+2 X^2+X+2  1 X^2+3  0 X^2+1  1 X+2  1  2 X^2+1 X^2+2 X+3 X^2+X+1 X+3 X^2+X X+3 X^2+1  1  2  1 X^2+X+2 X^2+3 X^2+X+1 X^2+X X^2+2 X^2+1  1 X+1  2 X^2+2  1  0
 0  0  0 X^2 X^2  2 X^2+2 X^2 X^2+2  0 X^2  2 X^2+2  0  2  0  2  2 X^2+2 X^2+2 X^2 X^2+2 X^2+2 X^2  0  0 X^2  2 X^2+2  0 X^2+2 X^2+2 X^2 X^2  0  2 X^2 X^2 X^2+2 X^2+2  0  2 X^2+2  2  2  2 X^2  2 X^2+2  0  0  0  2 X^2 X^2 X^2 X^2  0  0  2  0  0 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 60.

Homogenous weight enumerator: w(x)=1x^0+103x^60+586x^61+1029x^62+1690x^63+1868x^64+2258x^65+2134x^66+1896x^67+1582x^68+1442x^69+726x^70+516x^71+270x^72+152x^73+63x^74+18x^75+23x^76+8x^77+7x^78+6x^79+1x^80+2x^81+1x^82+2x^83

The gray image is a code over GF(2) with n=528, k=14 and d=240.
This code was found by Heurico 1.16 in 2.67 seconds.