The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  2  1  1  0  1  1  0  1  1  1  1  2  2  2  2  0  0  1  1  1  1  0  2  2  2  0  1  1  0  1  1  2  1
 0  1  1  0  3  1  2  3  1  2  1  1  0  3  1  0  3  1  2  2  1  1  1  1  0  2  2  0  0  2  3  1  1  1  0  2  2  0  3  1  2  1  1  0
 0  0  2  2  0  2  2  2  2  0  0  0  0  0  2  2  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0  0  2  2  0  0  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+6x^44+16x^45+6x^46+1x^48+2x^50

The gray image is a code over GF(2) with n=88, k=5 and d=44.
This code was found by Heurico 1.16 in 0.00942 seconds.