The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+492x^75+168x^76+336x^77+240x^78+828x^79+225x^80+192x^81+324x^83+144x^84+144x^85+144x^86+660x^87+102x^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 0.828 seconds.