The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+98x^44+252x^46+334x^48+288x^50+264x^52+222x^54+230x^56+138x^58+128x^60+54x^62+27x^64+6x^66+6x^68

The gray image is a code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 0.436 seconds.