The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+49x^22+94x^23+119x^24+168x^25+171x^26+152x^27+177x^28+192x^29+181x^30+188x^31+162x^32+136x^33+97x^34+72x^35+51x^36+16x^37+14x^38+6x^39+2x^40

The gray image is a code over GF(2) with n=58, k=11 and d=22.
This code was found by Heurico 1.16 in 0.173 seconds.