The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+26x^6+88x^7+87x^8+64x^9+140x^10+192x^11+143x^12+112x^13+90x^14+40x^15+24x^16+16x^17+1x^20

The gray image is a code over GF(2) with n=22, k=10 and d=6.
This code was found by Heurico 1.16 in 0.00525 seconds.