The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+19x^10+24x^11+35x^12+44x^13+22x^14+36x^15+25x^16+20x^17+23x^18+4x^19+3x^20

The gray image is a code over GF(2) with n=28, k=8 and d=10.
This code was found by Heurico 1.16 in 0.00137 seconds.