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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+59x^56+110x^58+80x^59+219x^60+272x^61+534x^62+368x^63+207x^64+48x^65+76x^66+45x^68+14x^70+12x^72+2x^74+1x^112

The gray image is a code over GF(2) with n=496, k=11 and d=224.
This code was found by Heurico 1.16 in 0.313 seconds.