The generator matrix

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

generates a code of length 19 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+31x^16+32x^18+47x^20+16x^24+1x^36

The gray image is a code over GF(2) with n=38, k=7 and d=16.
This code was found by Heurico 1.16 in 0.0022 seconds.