The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+204x^83+222x^84+276x^85+360x^86+456x^87+249x^88+360x^89+312x^90+288x^91+75x^92+132x^93+216x^94+264x^95+276x^96+192x^97+72x^98+132x^99+3x^100+6x^104

The gray image is a linear code over GF(4) with n=120, k=6 and d=83.
This code was found by Heurico 1.16 in 0.031 seconds.