The generator matrix

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

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+777x^72+852x^74+2004x^76+1476x^78+2943x^80+2268x^82+2940x^84+1452x^86+1551x^88+96x^90+24x^96

The gray image is a linear code over GF(4) with n=108, k=7 and d=72.
This code was found by Heurico 1.16 in 0.408 seconds.