The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+82x^20+90x^21+253x^22+314x^23+420x^24+480x^25+562x^26+704x^27+709x^28+860x^29+720x^30+804x^31+621x^32+520x^33+442x^34+208x^35+198x^36+90x^37+67x^38+18x^39+14x^40+8x^41+4x^42+3x^44

The gray image is a code over GF(2) with n=58, k=13 and d=20.
This code was found by Heurico 1.16 in 2.65 seconds.