The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^10+50x^11+147x^12+196x^13+175x^14+262x^15+252x^16+280x^17+251x^18+190x^19+105x^20+36x^21+37x^22+10x^23+7x^24+3x^26

The gray image is a code over GF(2) with n=32, k=11 and d=10.
This code was found by Heurico 1.16 in 0.0459 seconds.