The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^4+1128x^6+4006x^8+5752x^10+3964x^12+1176x^14+161x^16+8x^18

The gray image is a code over GF(2) with n=20, k=14 and d=4.
This code was found by Heurico 1.10 in 0.0341 seconds.