The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+71x^10+60x^11+131x^12+196x^13+199x^14+256x^15+205x^16+264x^17+223x^18+188x^19+136x^20+52x^21+49x^22+8x^23+6x^24+2x^26+1x^28

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 0.0507 seconds.