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  X  1  1  1  1 2X  1  1  1  1  1  1  X  1  X  0  X  1  X  0  1
 0  X  0 3X+2 2X+2 X+2  2  X 2X+2 3X+2  0 3X+2 2X 3X 2X+2  X  0 3X+2 2X+2  X X+2  2 3X 2X 3X+2  0 2X+2  X 3X  2  2  X X+2 2X+2 3X+2 2X 3X 2X X+2  X  0 3X+2 2X+2  X X+2 3X+2 3X+2  X 3X 3X 3X+2  X  X  X 3X+2 X+2 3X  X  0
 0  0  2  0 2X+2 2X+2 2X 2X+2 2X+2  0 2X  2 2X+2 2X+2 2X 2X  0 2X  2  2 2X+2 2X 2X 2X+2  0 2X 2X+2  2  0 2X+2  0  2  0  0  2  0 2X  0  2  2  2 2X  2 2X+2 2X 2X 2X+2 2X+2 2X+2  0 2X 2X  2 2X  0 2X+2  0  0  0
 0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0  0  0  0 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  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+61x^54+86x^55+205x^56+164x^57+316x^58+412x^59+310x^60+150x^61+192x^62+74x^63+56x^64+4x^65+5x^66+4x^67+4x^68+2x^69+1x^74+1x^102

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 0.296 seconds.