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  X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  X  1  1  X  1  X  1
 0  2  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  0  2  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  0  2  2  2  2  0  0  0  2  2  0  2  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  0  2  0  2  0  2  2  2  2  2  0  2  0  0  0  2  0  2  0  2  0  2  0  2  2  0  0  0  2  0  2  2  2  2  2  2  2  2  0  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  0  0  2  0  0  2  2  0  0  2  0  2  0  0  2  0  2  0  0  2  2  0  2  2  2  2  2  2  0  2  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2  2  0  2  2  2  2  2  0  2  2  0  2  2
 0  0  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  2  0  2  0  2  2  0  0  0  2  0  2  2  0  2  0  2  0  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  0  0  0  0  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  0  0  0  0  2  2  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  0  0  2  2  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  0  2  2  0  2  0  0  0  2  2  2  0  0  2  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  2  2  0  2  0  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2  2  2  0  0  2  0  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+117x^56+144x^60+1536x^62+178x^64+16x^68+55x^72+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 3.22 seconds.