The generator matrix

 1  0  0  1  1  1  0  1  1  1
 0  1  0  1  0  1  1  0  0  0
 0  0  1  1  1  0  1  0  0  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+52x^4+104x^6+128x^7+238x^8+384x^9+248x^10+384x^11+196x^12+128x^13+152x^14+25x^16+8x^18

The gray image is a code over GF(2) with n=20, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00658 seconds.