The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+30x^10+32x^11+79x^12+96x^13+102x^14+128x^15+99x^16+128x^17+90x^18+96x^19+72x^20+32x^21+34x^22+4x^24+1x^28

The gray image is a code over GF(2) with n=32, k=10 and d=10.
This code was found by Heurico 1.16 in 0.0123 seconds.