The generator matrix

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

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+38x^54+200x^55+110x^56+162x^57+239x^58+562x^59+238x^60+156x^61+98x^62+196x^63+33x^64+2x^65+8x^66+2x^67+2x^68+1x^106

The gray image is a code over GF(2) with n=472, k=11 and d=216.
This code was found by Heurico 1.16 in 0.25 seconds.