The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+570x^54+1832x^55+4794x^56+6872x^57+10600x^58+13820x^59+17840x^60+18216x^61+17848x^62+14596x^63+11111x^64+6248x^65+3824x^66+1668x^67+856x^68+216x^69+107x^70+20x^71+22x^72+8x^74+2x^78+1x^86

The gray image is a code over GF(2) with n=488, k=17 and d=216.
This code was found by Heurico 1.16 in 136 seconds.