The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1  1  1  X a*X  1  1 a*X  1  1  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a^2*X+1 X+a a*X+a^2  1  X a*X+1 a^2*X a*X+1  1  1 a^2*X  1  1  0 a^2*X+1  X
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X  X  0 a*X a*X  X a^2*X a*X  0 a^2*X  0  0  X a*X a^2*X a*X a^2*X

generates a code of length 27 over F4[X]/(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.