The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^20+122x^21+359x^22+440x^23+902x^24+1032x^25+1523x^26+1894x^27+2295x^28+2896x^29+2955x^30+3496x^31+2916x^32+3032x^33+2427x^34+1972x^35+1594x^36+994x^37+805x^38+368x^39+324x^40+112x^41+113x^42+22x^43+27x^44+4x^45+9x^46+1x^48+1x^50

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 36.1 seconds.