The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+124x^59+936x^60+2504x^61+4548x^62+7392x^63+10354x^64+13664x^65+16845x^66+17912x^67+17153x^68+14512x^69+10518x^70+6940x^71+4110x^72+1984x^73+890x^74+420x^75+138x^76+72x^77+26x^78+12x^79+9x^80+5x^82+1x^84+2x^88

The gray image is a code over GF(2) with n=536, k=17 and d=236.
This code was found by Heurico 1.16 in 148 seconds.