The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+70x^11+196x^12+396x^13+732x^14+1198x^15+1858x^16+2576x^17+3272x^18+3916x^19+4201x^20+3976x^21+3376x^22+2636x^23+1876x^24+1168x^25+664x^26+366x^27+186x^28+76x^29+20x^30+6x^31+1x^32+1x^36

The gray image is a code over GF(2) with n=40, k=15 and d=11.
This code was found by Heurico 1.16 in 15.6 seconds.