The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+98x^60+852x^61+2353x^62+4706x^63+8553x^64+14304x^65+21017x^66+27268x^67+33615x^68+35618x^69+34813x^70+27940x^71+21005x^72+13892x^73+8271x^74+4402x^75+1957x^76+918x^77+314x^78+120x^79+79x^80+10x^81+16x^82+10x^83+2x^84+4x^85+2x^87+2x^88+2x^89

The gray image is a code over GF(2) with n=552, k=18 and d=240.
This code was found by Heurico 1.16 in 623 seconds.