The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  4  1
 0  2  0  0  0  0  0  0  0  2  2  4  2  6
 0  0  2  0  0  0  0  4  6  2  6  6  4  6
 0  0  0  2  0  0  0  6  6  4  4  2  0  2
 0  0  0  0  2  0  0  2  0  0  2  4  6  4
 0  0  0  0  0  2  0  2  4  2  6  2  2  2
 0  0  0  0  0  0  2  2  4  2  0  0  6  4

generates a code of length 14 over Z8 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+82x^7+260x^8+452x^9+731x^10+1236x^11+1842x^12+6404x^13+10742x^14+6440x^15+1771x^16+1260x^17+804x^18+428x^19+222x^20+76x^21+10x^22+6x^23+1x^26

The gray image is a code over GF(2) with n=56, k=15 and d=14.
This code was found by Heurico 1.16 in 2.16 seconds.