The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  1  1  1  1  0  X  0  1  1  1  1  1 (a+1)X  1  1  1  1  X  1  1  1  1  X  1  1  1
 0  1  0  0  X (a+1)X  1  a a+1 (a+1)X+1 (a+1)X+a+1 X+a  1  1 (a+1)X+1 (a+1)X+a (a+1)X+a+1 aX+a a+1  1  1 (a+1)X aX+a+1  X X+a  X X+1  1 aX+a+1  0 (a+1)X+a X+1  1 aX  a (a+1)X+a aX aX aX+a  X (a+1)X+a+1
 0  0  1  1 (a+1)X+a a+1 X+a+1  a X+1  a X+a (a+1)X (a+1)X+1  1 aX X+a+1  0 aX+1 (a+1)X+a+1 a+1 X+a  1 a+1  0  X aX+1 (a+1)X+a+1  X (a+1)X+a X+a aX+1 aX+a (a+1)X+a+1 X+1 aX+1 a+1 aX  1 aX (a+1)X+1 X+a
 0  0  0 (a+1)X  0 aX aX  0 (a+1)X aX (a+1)X  0  0  X  0  X  X  0 aX aX  0 (a+1)X (a+1)X (a+1)X aX  X (a+1)X aX  X  X (a+1)X  X  X aX aX  0  X (a+1)X aX aX  X

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+450x^112+144x^113+180x^114+396x^115+1377x^116+588x^117+336x^118+780x^119+2022x^120+780x^121+324x^122+804x^123+2070x^124+852x^125+348x^126+660x^127+1755x^128+564x^129+312x^130+384x^131+897x^132+144x^133+36x^134+48x^135+105x^136+24x^140+3x^152

The gray image is a linear code over GF(4) with n=164, k=7 and d=112.
This code was found by Heurico 1.16 in 0.536 seconds.