The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+216x^55+444x^56+762x^57+519x^58+588x^59+435x^60+396x^61+287x^62+264x^63+79x^64+42x^65+24x^66+36x^67+1x^70+1x^76+1x^82

The gray image is a code over GF(2) with n=472, k=12 and d=220.
This code was found by Heurico 1.16 in 0.343 seconds.