The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+530x^55+875x^56+1290x^57+1183x^58+1306x^59+843x^60+772x^61+422x^62+426x^63+263x^64+162x^65+57x^66+50x^67+1x^68+8x^69+2x^70+1x^72

The gray image is a code over GF(2) with n=472, k=13 and d=220.
This code was found by Heurico 1.16 in 34 seconds.