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

generates a code of length 40 over GR(16,4) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+156x^112+108x^116+396x^120+324x^124+27x^128+12x^144

The gray image is a code over GF(4) with n=160, k=5 and d=112.
This code was found by Heurico 1.16 in 0.015 seconds.