The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+66x^23+106x^24+64x^25+170x^26+252x^27+136x^28+80x^29+188x^30+272x^31+191x^32+96x^33+144x^34+164x^35+56x^36+16x^37+4x^38+14x^39+22x^40+6x^42

The gray image is a code over GF(2) with n=60, k=11 and d=23.
This code was found by Heurico 1.16 in 65.1 seconds.