The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+48x^29+28x^30+31x^32+16x^37+4x^38

The gray image is a code over GF(2) with n=62, k=7 and d=29.
This code was found by Heurico 1.16 in 15.2 seconds.