The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+183x^72+309x^76+432x^80+192x^81+507x^84+1728x^85+549x^88+5184x^89+591x^92+5184x^93+651x^96+477x^100+237x^104+132x^108+24x^112+3x^120

The gray image is a linear code over GF(4) with n=120, k=7 and d=72.
This code was found by Heurico 1.16 in 1.08 seconds.