The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+138x^76+48x^79+609x^80+48x^81+288x^83+1329x^84+432x^85+768x^87+2868x^88+1296x^89+1248x^91+3084x^92+1296x^93+720x^95+1824x^96+249x^100+78x^104+48x^108+12x^112

The gray image is a linear code over GF(4) with n=120, k=7 and d=76.
This code was found by Heurico 1.16 in 0.568 seconds.