The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+130x^58+852x^59+2266x^60+4712x^61+8609x^62+14074x^63+21212x^64+28222x^65+32816x^66+35272x^67+34128x^68+28478x^69+21419x^70+14338x^71+8133x^72+4016x^73+1952x^74+908x^75+324x^76+150x^77+60x^78+40x^79+16x^80+4x^82+4x^83+4x^85+2x^86+2x^89

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 585 seconds.