The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 (a+1)X (a+1)X  1  1  1  1  X  1  1  1  1  1 (a+1)X  1  0  1
 0  1  0  0  X (a+1)X  1  a X+a a+1  1  1  1 (a+1)X+1 (a+1)X+a (a+1)X+a (a+1)X+1  1 (a+1)X+a+1 (a+1)X (a+1)X+a+1 aX+a+1 a+1  1 aX  1 a+1
 0  0  1  1 (a+1)X+a a+1 X+a+1  a (a+1)X  1 aX+1 X+a+1  1  a aX+1 a+1  0 aX+a  X X+1 X+a X+a+1  X (a+1)X+1  a (a+1)X (a+1)X+a+1
 0  0  0 (a+1)X  0 aX aX  0  0 aX  X  X aX  X aX  X (a+1)X  0 (a+1)X  X  X  0  0 (a+1)X (a+1)X (a+1)X  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+786x^72+576x^74+2616x^76+1152x^78+3057x^80+1728x^82+3528x^84+1152x^86+1767x^88+18x^96+3x^104

The gray image is a linear code over GF(4) with n=108, k=7 and d=72.
This code was found by Heurico 1.16 in 0.337 seconds.