The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+66x^22+134x^23+135x^24+210x^25+285x^26+282x^27+339x^28+394x^29+384x^30+386x^31+378x^32+330x^33+264x^34+198x^35+125x^36+86x^37+50x^38+24x^39+14x^40+4x^41+7x^42

The gray image is a code over GF(2) with n=60, k=12 and d=22.
This code was found by Heurico 1.16 in 0.731 seconds.