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

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+57x^56+114x^58+32x^59+210x^60+352x^61+562x^62+352x^63+197x^64+32x^65+60x^66+37x^68+26x^70+8x^72+6x^74+1x^76+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 0.312 seconds.