The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+2x^54+8x^55+3x^56+2x^58

The gray image is a code over GF(2) with n=104, k=4 and d=54.
This code was found by Heurico 1.16 in 0.0163 seconds.