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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+68x^53+27x^54+54x^56+140x^57+176x^58+1152x^59+176x^60+116x^61+50x^62+24x^64+36x^65+24x^69+3x^70+1x^112

The gray image is a code over GF(2) with n=472, k=11 and d=212.
This code was found by Heurico 1.16 in 5.39 seconds.