The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+51x^8+32x^9+84x^10+128x^11+112x^12+192x^13+136x^14+128x^15+83x^16+32x^17+36x^18+8x^20+1x^24

The gray image is a code over GF(2) with n=26, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00704 seconds.