The generator matrix

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

generates a code of length 32 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+80x^22+122x^23+313x^24+432x^25+557x^26+740x^27+945x^28+1156x^29+1410x^30+1604x^31+1538x^32+1632x^33+1434x^34+1288x^35+1042x^36+760x^37+516x^38+306x^39+235x^40+112x^41+97x^42+36x^43+21x^44+4x^45+2x^46+1x^48

The gray image is a code over GF(2) with n=64, k=14 and d=22.
This code was found by Heurico 1.16 in 23.4 seconds.