The generator matrix

 1  1  1  1  1  1  1  1  2  1  2  2  1  1
 0  2  0  0  0  0  0  2  2  2  2  2  0  0
 0  0  2  0  0  0  2  2  2  2  0  0  0  0
 0  0  0  2  0  0  2  0  0  2  2  2  0  2
 0  0  0  0  2  0  2  0  2  0  0  2  2  2
 0  0  0  0  0  2  2  0  2  0  2  0  2  0

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

Homogenous weight enumerator: w(x)=1x^0+10x^10+8x^11+18x^12+24x^13+14x^14+24x^15+7x^16+8x^17+6x^18+6x^20+2x^22

The gray image is a code over GF(2) with n=28, k=7 and d=10.
This code was found by Heurico 1.16 in 0.00109 seconds.