The generator matrix

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

generates a code of length 44 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+48x^118+567x^120+540x^122+1116x^124+888x^126+1869x^128+1416x^130+2820x^132+1584x^134+2499x^136+1404x^138+1074x^140+264x^142+147x^144+48x^148+54x^152+30x^156+15x^160

The gray image is a linear code over GF(4) with n=176, k=7 and d=118.
This code was found by Heurico 1.16 in 51.4 seconds.