The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+83x^20+102x^21+376x^22+362x^23+589x^24+764x^25+904x^26+1174x^27+1352x^28+1652x^29+1509x^30+1724x^31+1373x^32+1248x^33+1048x^34+740x^35+603x^36+310x^37+234x^38+90x^39+85x^40+20x^41+24x^42+6x^43+10x^44+1x^46

The gray image is a code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.16 in 19.8 seconds.