The generator matrix

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

generates a code of length 31 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+137x^20+126x^21+411x^22+498x^23+896x^24+1000x^25+1536x^26+1886x^27+2298x^28+2962x^29+2871x^30+3420x^31+2848x^32+2984x^33+2440x^34+1924x^35+1605x^36+1002x^37+841x^38+434x^39+366x^40+112x^41+88x^42+30x^43+40x^44+6x^45+5x^46+1x^48

The gray image is a code over GF(2) with n=62, k=15 and d=20.
This code was found by Heurico 1.16 in 49.7 seconds.