The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^10+72x^11+87x^12+128x^13+143x^14+112x^15+103x^16+128x^17+101x^18+72x^19+32x^20+5x^22+1x^28

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 0.0133 seconds.