The generator matrix

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

generates a code of length 12 over GR(16,4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+156x^25+240x^27+1068x^28+816x^29+864x^30+2160x^31+3306x^32+3912x^33+5184x^34+6480x^35+11220x^36+8304x^37+7776x^38+6480x^39+5358x^40+2172x^41+24x^44+15x^48

The gray image is a code over GF(4) with n=48, k=8 and d=25.
This code was found by Heurico 1.16 in 1.75 seconds.