The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+130x^61+1039x^62+2402x^63+4850x^64+7236x^65+10775x^66+13818x^67+16886x^68+17512x^69+16329x^70+14048x^71+10948x^72+6702x^73+4569x^74+2186x^75+912x^76+408x^77+204x^78+58x^79+31x^80+10x^81+12x^82+2x^84+2x^88+2x^93

The gray image is a code over GF(2) with n=552, k=17 and d=244.
This code was found by Heurico 1.16 in 149 seconds.