The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+168x^81+96x^82+180x^83+87x^84+492x^85+204x^86+168x^87+78x^88+540x^89+156x^90+144x^91+36x^92+804x^93+228x^94+216x^95+21x^96+300x^97+84x^98+60x^99+6x^100+6x^104+12x^108+6x^112+3x^116

The gray image is a linear code over GF(4) with n=120, k=6 and d=81.
This code was found by Heurico 1.16 in 1.69 seconds.