The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+456x^75+180x^76+336x^77+240x^78+936x^79+189x^80+192x^81+216x^83+180x^84+144x^85+144x^86+696x^87+90x^88+96x^89

The gray image is a linear code over GF(4) with n=108, k=6 and d=75.
This code was found by Heurico 1.16 in 0.016 seconds.