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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+165x^56+48x^58+598x^60+512x^61+464x^62+184x^64+66x^68+9x^72+1x^112

The gray image is a code over GF(2) with n=488, k=11 and d=224.
This code was found by Heurico 1.16 in 11.9 seconds.