The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+94x^22+106x^23+206x^24+306x^25+414x^26+490x^27+584x^28+708x^29+716x^30+848x^31+783x^32+760x^33+620x^34+512x^35+400x^36+252x^37+182x^38+86x^39+66x^40+22x^41+22x^42+6x^43+8x^44

The gray image is a code over GF(2) with n=62, k=13 and d=22.
This code was found by Heurico 1.16 in 3.08 seconds.