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

generates a code of length 40 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+348x^113+336x^114+168x^115+9x^116+576x^117+696x^118+252x^119+24x^120+312x^121+360x^122+48x^123+27x^124+144x^125+168x^126+60x^127+348x^129+168x^130+48x^131+3x^136

The gray image is a linear code over GF(4) with n=160, k=6 and d=113.
This code was found by Heurico 1.16 in 0.047 seconds.