The generator matrix

 1  0  0  0  0  0  1  1  1  2  0  2  1  1  0  1  0  1  1  0  1  2  1  1  0  1  1  1  2  1  1
 0  1  0  0  0  0  0  0  0  0  1  2  1  3  1  1  1  0  1  0  2  2  3  2  1  0  3  2  2  1  0
 0  0  1  0  0  0  0  0  0  0  0  1  1  2  3  1  2  3  3  2  0  1  0  2  1  1  1  1  1  1  0
 0  0  0  1  0  0  0  1  1  1  2  2  0  1  1  2  2  3  3  2  1  1  2  1  2  2  1  1  0  1  2
 0  0  0  0  1  0  1  1  0  3  2  0  1  2  0  0  1  2  3  1  1  3  3  0  1  1  0  1  3  3  2
 0  0  0  0  0  1  1  2  3  1  3  1  3  0  2  1  2  3  1  3  3  1  0  0  0  3  2  2  2  0  0
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  0  0  0  2  2  0  0  0  2  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+66x^22+100x^23+231x^24+378x^25+409x^26+438x^27+599x^28+700x^29+700x^30+810x^31+759x^32+748x^33+701x^34+546x^35+383x^36+268x^37+149x^38+82x^39+68x^40+18x^41+22x^42+8x^43+6x^44+1x^46+1x^48

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 3.12 seconds.