The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+61x^8+58x^9+113x^10+140x^11+219x^12+334x^13+249x^14+264x^15+190x^16+182x^17+139x^18+44x^19+41x^20+2x^21+11x^22

The gray image is a code over GF(2) with n=28, k=11 and d=8.
This code was found by Heurico 1.16 in 0.0249 seconds.