The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+92x^10+340x^12+64x^13+860x^14+1344x^15+1950x^16+1344x^17+3192x^18+6720x^19+3592x^20+2240x^21+3032x^22+4032x^23+2000x^24+448x^25+940x^26+192x^27+292x^28+76x^30+17x^32

The gray image is a code over GF(2) with n=40, k=15 and d=10.
This code was found by Heurico 1.16 in 6.53 seconds.