The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+144x^58+1084x^59+2367x^60+4526x^61+7478x^62+10850x^63+13574x^64+16296x^65+17683x^66+16972x^67+14824x^68+10684x^69+6812x^70+4094x^71+1891x^72+1074x^73+445x^74+170x^75+39x^76+26x^77+12x^78+10x^79+8x^80+2x^81+2x^82+2x^83+2x^87

The gray image is a code over GF(2) with n=528, k=17 and d=232.
This code was found by Heurico 1.16 in 133 seconds.