The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+51x^58+896x^59+2272x^60+5116x^61+8591x^62+14182x^63+19859x^64+28086x^65+33170x^66+36672x^67+33916x^68+28818x^69+20623x^70+14322x^71+7558x^72+4436x^73+1952x^74+956x^75+448x^76+122x^77+48x^78+12x^79+10x^80+10x^81+11x^82+4x^85+2x^86

The gray image is a code over GF(2) with n=536, k=18 and d=232.
This code was found by Heurico 1.16 in 617 seconds.