The generator matrix

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

generates a code of length 40 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+48x^104+168x^107+246x^108+48x^109+312x^110+300x^111+738x^112+288x^113+672x^114+552x^115+588x^116+768x^117+1872x^118+504x^119+777x^120+1248x^121+2208x^122+792x^123+915x^124+720x^125+1080x^126+636x^127+483x^128+120x^131+168x^132+57x^136+45x^140+24x^144+6x^148

The gray image is a linear code over GF(4) with n=160, k=7 and d=104.
This code was found by Heurico 1.16 in 0.805 seconds.