The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+144x^77+372x^78+648x^79+891x^80+1188x^81+1848x^82+2244x^83+1635x^84+3204x^85+3144x^86+3780x^87+2907x^88+6300x^89+5040x^90+5292x^91+3768x^92+7260x^93+5028x^94+3876x^95+2211x^96+1872x^97+1464x^98+1056x^99+339x^100+3x^104+18x^108+3x^112

The gray image is a linear code over GF(4) with n=120, k=8 and d=77.
This code was found by Heurico 1.16 in 6.17 seconds.