The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+105x^72+72x^73+96x^74+510x^76+360x^77+192x^78+348x^80+600x^81+288x^82+540x^84+504x^85+192x^86+237x^88+30x^92+21x^96

The gray image is a linear code over GF(4) with n=108, k=6 and d=72.
This code was found by Heurico 1.16 in 0.035 seconds.