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

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+153x^112+375x^116+444x^120+1035x^124+3027x^128+5688x^132+4332x^136+438x^140+369x^144+291x^148+168x^152+39x^156+18x^160+6x^164

The gray image is a code over GF(4) with n=176, k=7 and d=112.
This code was found by Heurico 1.16 in 1.81 seconds.