The generator matrix

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

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+120x^72+36x^73+132x^74+276x^75+1188x^76+480x^77+648x^78+1068x^79+3348x^80+1560x^81+1896x^82+2376x^83+6345x^84+3600x^85+4080x^86+4056x^87+9537x^88+4452x^89+4404x^90+3684x^91+6552x^92+2160x^93+1128x^94+828x^95+1455x^96+57x^100+45x^104+18x^108+6x^112

The gray image is a linear code over GF(4) with n=116, k=8 and d=72.
This code was found by Heurico 1.16 in 7.17 seconds.