The generator matrix

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

generates a code of length 31 over GR(16,4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+141x^88+192x^90+576x^94+87x^96+24x^112+3x^120

The gray image is a code over GF(4) with n=124, k=5 and d=88.
This code was found by Heurico 1.16 in 1.97 seconds.