The generator matrix

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

generates a code of length 25 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+46x^14+214x^15+420x^16+764x^17+1219x^18+1782x^19+2775x^20+3856x^21+5011x^22+6310x^23+6913x^24+6916x^25+6862x^26+6264x^27+5046x^28+3884x^29+2884x^30+1886x^31+1145x^32+688x^33+351x^34+178x^35+83x^36+20x^37+11x^38+6x^39+1x^40

The gray image is a code over GF(2) with n=50, k=16 and d=14.
This code was found by Heurico 1.10 in 36.6 seconds.