The generator matrix

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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+519x^112+912x^113+696x^114+684x^115+2979x^116+3516x^117+2628x^118+2064x^119+7293x^120+9456x^121+5592x^122+4032x^123+14757x^124+17592x^125+10404x^126+7368x^127+23325x^128+25200x^129+14472x^130+9132x^131+23478x^132+22188x^133+11148x^134+5952x^135+14223x^136+11376x^137+3816x^138+1416x^139+3276x^140+1920x^141+396x^142+72x^143+186x^144+51x^148+12x^152+3x^156+9x^160

The gray image is a linear code over GF(4) with n=172, k=9 and d=112.
This code was found by Heurico 1.16 in 151 seconds.