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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+300x^116+72x^117+156x^119+1203x^120+348x^121+336x^123+1488x^124+528x^125+936x^127+2610x^128+984x^129+1104x^131+2637x^132+840x^133+540x^135+1575x^136+300x^137+270x^140+66x^144+45x^148+24x^152+12x^156+9x^160

The gray image is a linear code over GF(4) with n=172, k=7 and d=116.
This code was found by Heurico 1.16 in 1.31 seconds.