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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+63x^52+100x^56+352x^58+1024x^59+405x^60+32x^62+27x^64+25x^68+16x^72+2x^76+1x^108

The gray image is a code over GF(2) with n=472, k=11 and d=208.
This code was found by Heurico 1.16 in 0.235 seconds.