The generator matrix

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

generates a code of length 23 over GR(16,4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+204x^54+132x^55+690x^56+852x^57+1512x^58+2220x^59+3954x^60+3708x^61+6156x^62+7368x^63+11115x^64+11688x^65+17040x^66+18552x^67+24252x^68+25560x^69+26244x^70+23412x^71+24528x^72+17604x^73+15048x^74+9756x^75+6984x^76+2028x^77+1380x^78+108x^80+36x^84+6x^88+6x^92

The gray image is a code over GF(4) with n=92, k=9 and d=54.
This code was found by Heurico 1.16 in 64.9 seconds.