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

generates a code of length 59 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+37x^56+144x^58+640x^59+179x^60+16x^62+6x^64+1x^116

The gray image is a code over GF(2) with n=472, k=10 and d=224.
This code was found by Heurico 1.16 in 0.203 seconds.