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

generates a code of length 42 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+13x^44+1x^48+1x^52

The gray image is a code over GF(2) with n=84, k=4 and d=44.
This code was found by Heurico 1.16 in 0.011 seconds.