The generator matrix

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

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+81x^24+324x^28+576x^30+456x^32+1536x^33+5184x^34+750x^36+9216x^37+15552x^38+1143x^40+13824x^41+15552x^42+840x^44+399x^48+102x^52

The gray image is a code over GF(4) with n=52, k=8 and d=24.
This code was found by Heurico 1.16 in 1.69 seconds.