The generator matrix

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

generates a code of length 27 over F4[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+66x^72+216x^73+300x^76+720x^77+201x^80+1056x^81+276x^84+1008x^85+132x^88+72x^89+24x^92+24x^96

The gray image is a linear code over GF(4) with n=108, k=6 and d=72.
This code was found by Heurico 1.16 in 0.0353 seconds.