The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  2  2  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  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+61x^8+126x^10+274x^12+597x^14+973x^16+1364x^18+4096x^19+1436x^20+4096x^21+1287x^22+1019x^24+574x^26+306x^28+131x^30+26x^32+16x^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 1.8 seconds.