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

generates a code of length 62 over Z4[X]/(X^3+2,2X) 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 0.297 seconds.