The generator matrix

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

generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+498x^72+564x^73+732x^74+1404x^75+2916x^76+3084x^77+3132x^78+4416x^79+8913x^80+9780x^81+9168x^82+9624x^83+19509x^84+20376x^85+17688x^86+15456x^87+28908x^88+26364x^89+17820x^90+13836x^91+19551x^92+12540x^93+6636x^94+4416x^95+3561x^96+1020x^97+120x^98+51x^100+30x^104+21x^108+9x^112

The gray image is a linear code over GF(4) with n=116, k=9 and d=72.
This code was found by Heurico 1.16 in 86.7 seconds.