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

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

Homogenous weight enumerator: w(x)=1x^0+56x^44+6x^48+1x^64

The gray image is a code over GF(2) with n=88, k=6 and d=44.
This code was found by Heurico 1.16 in 8.93 seconds.