The generator matrix

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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+84x^115+99x^116+276x^117+456x^118+516x^119+111x^120+300x^121+456x^122+336x^123+105x^124+72x^125+180x^126+192x^127+54x^128+252x^129+144x^130+156x^131+66x^132+60x^133+108x^134+60x^135+6x^136+6x^140

The gray image is a linear code over GF(4) with n=164, k=6 and d=115.
This code was found by Heurico 1.16 in 0.0395 seconds.