The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+36x^4+40x^6+64x^7+126x^8+192x^9+120x^10+192x^11+84x^12+64x^13+88x^14+9x^16+8x^18

The gray image is a code over GF(2) with n=20, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00327 seconds.