The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  2  1  1  2  1  1  2  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0
 0  1  1  0  3  1  0  3  1  0  1  1  2  3  1  2  3  1  2  1  1  2  1  1  0  0  0  0  2  2  2  2  3  3  3  3  1  1  1  1  0  0  0  2  2  2  0  2  1  1  1  1  1  1  1
 0  0  2  0  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  0  0  2
 0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  2  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2

generates a code of length 55 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+12x^54+32x^55+14x^56+2x^62+1x^64+2x^70

The gray image is a code over GF(2) with n=110, k=6 and d=54.
This code was found by Heurico 1.16 in 0.022 seconds.