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 2X  1  1  1  1  1  1  1  1
 0  X  0 X+2 2X 3X+2  0  X 2X+2 3X+2  2  X 2X+2 3X+2 2X+2 3X  0 X+2 2X 3X+2 X+2 2X 2X+2  X  2 3X  2 3X  0 3X+2 2X+2  X  0 3X+2  X 2X+2  0  X 2X+2 3X+2 2X+2  X 3X 3X  2  X  2 2X+2 2X+2  X 2X X+2 2X  0 2X 3X+2 3X+2  0  2
 0  0  2  0  0  2 2X+2 2X+2 2X+2 2X  2 2X 2X  2 2X 2X+2  0 2X+2  2 2X 2X+2 2X+2  0  0  0  0  2 2X+2 2X  0 2X+2 2X+2 2X 2X  2 2X  2  2  2  0 2X 2X  2  2  2 2X 2X+2 2X+2  0  0  0 2X 2X+2 2X 2X  2 2X+2 2X+2  0
 0  0  0  2 2X+2  2 2X+2  0  0  0 2X+2  2 2X+2  0  0  2 2X  0  2 2X 2X+2  0 2X+2  2  2 2X+2  2 2X+2 2X 2X 2X 2X 2X+2 2X+2  0 2X 2X+2  2 2X  0  2 2X+2 2X+2 2X  0  0  2 2X+2 2X 2X  0  2 2X  2  0 2X+2 2X  2  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+108x^55+87x^56+108x^57+832x^58+88x^59+551x^60+56x^61+16x^62+60x^63+48x^64+92x^65+1x^116

The gray image is a code over GF(2) with n=472, k=11 and d=220.
This code was found by Heurico 1.16 in 9 seconds.