The generator matrix

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

generates a code of length 44 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+432x^115+819x^116+804x^117+816x^118+3348x^119+3414x^120+2568x^121+2616x^122+8832x^123+7041x^124+4908x^125+6120x^126+16776x^127+13497x^128+9192x^129+10728x^130+26880x^131+18552x^132+11772x^133+12288x^134+27732x^135+17556x^136+8952x^137+8520x^138+16848x^139+9060x^140+4212x^141+1704x^142+3504x^143+1644x^144+600x^145+216x^146+96x^147+27x^148+36x^152+15x^156+6x^160+6x^164+6x^168

The gray image is a linear code over GF(4) with n=176, k=9 and d=115.
This code was found by Heurico 1.16 in 162 seconds.