The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+316x^55+1134x^56+2004x^57+2821x^58+3876x^59+4438x^60+4448x^61+3973x^62+3690x^63+2720x^64+1578x^65+891x^66+448x^67+236x^68+124x^69+35x^70+22x^71+7x^72+6x^73

The gray image is a code over GF(2) with n=488, k=15 and d=220.
This code was found by Heurico 1.16 in 10.1 seconds.