The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+437x^54+930x^55+1692x^56+2164x^57+2277x^58+2144x^59+2118x^60+1672x^61+1301x^62+790x^63+450x^64+184x^65+126x^66+40x^67+40x^68+12x^69+3x^72+3x^74

The gray image is a code over GF(2) with n=472, k=14 and d=216.
This code was found by Heurico 1.16 in 2.78 seconds.