The generator matrix

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

generates a code of length 25 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+198x^16+576x^18+1512x^20+2290x^22+3602x^24+3432x^26+2744x^28+1244x^30+597x^32+136x^34+48x^36+2x^38+2x^40

The gray image is a code over GF(2) with n=50, k=14 and d=16.
This code was found by Heurico 1.16 in 12 seconds.