The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+120x^76+72x^77+144x^79+282x^80+72x^81+192x^84+24x^85+48x^87+36x^88+24x^89+9x^96

The gray image is a linear code over GF(4) with n=108, k=5 and d=76.
This code was found by Heurico 1.16 in 0.016 seconds.