The generator matrix

 1  0  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  0  1  1  1  1  1  1  1  1  X  1  1
 0  1  1  a a+1  0 (a+1)X+1  a  1 (a+1)X+a+1 (a+1)X+1  a  1  0 (a+1)X+a+1 (a+1)X+1  a  1 (a+1)X+a+1  0 (a+1)X+a+1 (a+1)X+1 X+1 X+a+1 aX+a+1 X+a+1  1  X  0
 0  0 (a+1)X  0  0  0  X aX aX  X  X  X  X (a+1)X (a+1)X (a+1)X  X  X aX  X  0  X aX aX  0 aX (a+1)X aX  0
 0  0  0  X  0  X (a+1)X  X aX aX aX (a+1)X  0 (a+1)X (a+1)X  X (a+1)X  0  0  0 aX aX aX  X aX (a+1)X (a+1)X (a+1)X  0
 0  0  0  0 (a+1)X (a+1)X (a+1)X aX  X  0 aX  X aX (a+1)X  0 (a+1)X  0  0 aX  X  X (a+1)X (a+1)X  0 (a+1)X  0 (a+1)X  X  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+36x^72+12x^73+84x^75+177x^76+264x^77+516x^79+447x^80+744x^81+1128x^83+1017x^84+1824x^85+2280x^87+1326x^88+2220x^89+1860x^91+831x^92+1080x^93+276x^95+117x^96+75x^100+54x^104+12x^108+3x^112

The gray image is a linear code over GF(4) with n=116, k=7 and d=72.
This code was found by Heurico 1.16 in 0.541 seconds.