The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+116x^59+802x^60+2206x^61+4537x^62+8756x^63+13700x^64+20836x^65+28175x^66+33766x^67+36300x^68+34182x^69+27744x^70+21052x^71+14405x^72+8260x^73+3943x^74+1996x^75+774x^76+340x^77+141x^78+56x^79+30x^80+12x^81+4x^82+2x^83+2x^84+4x^85+2x^88

The gray image is a code over GF(2) with n=544, k=18 and d=236.
This code was found by Heurico 1.16 in 617 seconds.