The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+100x^8+125x^10+648x^12+128x^13+963x^14+896x^15+2086x^16+2688x^17+2669x^18+4480x^19+3152x^20+4480x^21+2859x^22+2688x^23+1764x^24+896x^25+1279x^26+128x^27+424x^28+273x^30+17x^32+23x^34+1x^38

The gray image is a code over GF(2) with n=40, k=15 and d=8.
This code was found by Heurico 1.16 in 4.17 seconds.