The generator matrix

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

generates a code of length 24 over GR(16,4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+219x^56+387x^60+474x^64+768x^66+549x^68+4608x^70+636x^72+6912x^74+741x^76+630x^80+315x^84+117x^88+24x^92+3x^96

The gray image is a code over GF(4) with n=96, k=7 and d=56.
This code was found by Heurico 1.16 in 3.14 seconds.