The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  0  0  0  1  1  1  1  2  0  2  0  2  0  2  1  1  1  1  2  2  2  2  0  0  0  2  2  2  2  2  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0

generates a code of length 54 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+3x^56+6x^57+4x^58+2x^61

The gray image is a code over GF(2) with n=108, k=4 and d=56.
This code was found by Heurico 1.16 in 0.0198 seconds.