The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+51x^10+179x^12+64x^13+426x^14+448x^15+926x^16+1344x^17+1565x^18+2240x^19+1875x^20+2240x^21+1580x^22+1344x^23+952x^24+448x^25+429x^26+64x^27+153x^28+42x^30+9x^32+3x^34+1x^36

The gray image is a code over GF(2) with n=40, k=14 and d=10.
This code was found by Heurico 1.16 in 13.3 seconds.