The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+62x^15+112x^16+84x^17+88x^18+102x^19+139x^20+124x^21+56x^22+90x^23+91x^24+44x^25+16x^26+2x^27+9x^28+4x^29

The gray image is a code over GF(2) with n=40, k=10 and d=15.
This code was found by Heurico 1.10 in 9.3 seconds.