The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^42+26x^44+40x^46+2x^48+4x^50+1x^52+1x^56+1x^60

The gray image is a code over GF(2) with n=88, k=7 and d=42.
This code was found by Heurico 1.16 in 0.019 seconds.