The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+84x^68+600x^71+213x^72+1392x^75+627x^76+3744x^79+1437x^80+4368x^83+1443x^84+2184x^87+81x^88+129x^92+54x^96+21x^100+6x^104

The gray image is a linear code over GF(4) with n=108, k=7 and d=68.
This code was found by Heurico 1.16 in 0.504 seconds.