The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+374x^53+1725x^54+4124x^55+7658x^56+13800x^57+19699x^58+28978x^59+34378x^60+39134x^61+35520x^62+30012x^63+20486x^64+13580x^65+6693x^66+3376x^67+1610x^68+704x^69+191x^70+48x^71+25x^72+8x^73+10x^74+6x^75+2x^76+2x^78

The gray image is a code over GF(2) with n=488, k=18 and d=212.
This code was found by Heurico 1.16 in 525 seconds.