The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  1  2  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  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  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  0

generates a code of length 20 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+76x^8+57x^10+408x^12+427x^14+256x^15+1166x^16+1280x^17+1201x^18+2560x^19+1456x^20+2560x^21+1435x^22+1280x^23+796x^24+256x^25+771x^26+184x^28+185x^30+9x^32+19x^34+1x^38

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 1.29 seconds.