The generator matrix

 1  0  0  0  1  1  1  1  1  1  1 2a+2  1
 0  1  0  0  1 2a+2 2a+2  1 3a+2  3 a+1  1  0
 0  0  1  0 3a+3  1  a 3a+3  1 2a+2 2a 2a+1  3
 0  0  0  1  1  a 3a+1  0 2a 3a+3 3a  2 a+1
 0  0  0  0 2a+2 2a  2  2 2a+2 2a 2a+2 2a+2  0

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+96x^25+204x^27+744x^28+624x^29+1152x^30+2448x^31+2805x^32+5376x^33+10368x^34+11016x^35+17100x^36+24096x^37+31104x^38+25104x^39+36480x^40+34080x^41+31104x^42+16524x^43+8256x^44+3312x^45+138x^48+12x^52

The gray image is a code over GF(4) with n=52, k=9 and d=25.
This code was found by Heurico 1.16 in 24.4 seconds.