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

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+96x^109+348x^110+600x^111+258x^112+672x^113+1104x^114+1128x^115+432x^116+900x^117+1236x^118+1296x^119+429x^120+948x^121+1308x^122+1248x^123+438x^124+876x^125+960x^126+888x^127+201x^128+348x^129+420x^130+216x^131+12x^132+9x^136+6x^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 0.603 seconds.