The generator matrix

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

generates a code of length 40 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+120x^109+432x^110+348x^111+582x^112+456x^113+1104x^114+648x^115+999x^116+756x^117+1692x^118+756x^119+1032x^120+708x^121+1260x^122+636x^123+921x^124+804x^125+1188x^126+576x^127+447x^128+228x^129+468x^130+108x^131+93x^132+12x^136+3x^140+6x^144

The gray image is a linear code over GF(4) with n=160, k=7 and d=109.
This code was found by Heurico 1.16 in 1.25 seconds.