The generator matrix

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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+192x^114+660x^115+324x^116+276x^117+1116x^118+2148x^119+810x^120+864x^121+2484x^122+3936x^123+1233x^124+1752x^125+4752x^126+6204x^127+1443x^128+2928x^129+6264x^130+7428x^131+1827x^132+2484x^133+5004x^134+5388x^135+1074x^136+912x^137+1620x^138+1704x^139+321x^140+72x^142+180x^143+54x^144+21x^148+36x^152+18x^156+6x^160

The gray image is a linear code over GF(4) with n=172, k=8 and d=114.
This code was found by Heurico 1.16 in 25 seconds.