The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+198x^64+351x^68+48x^69+441x^72+576x^73+558x^76+2592x^77+546x^80+5184x^81+696x^84+3888x^85+630x^88+426x^92+159x^96+81x^100+9x^104

The gray image is a linear code over GF(4) with n=108, k=7 and d=64.
This code was found by Heurico 1.16 in 1 seconds.