The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+80x^11+88x^12+102x^13+126x^14+136x^15+136x^16+132x^17+81x^18+56x^19+30x^20+6x^21+8x^22+1x^24+1x^26

The gray image is a code over GF(2) with n=30, k=10 and d=10.
This code was found by Heurico 1.16 in 1.36 seconds.