The generator matrix

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

generates a code of length 30 over F4[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+210x^80+516x^81+300x^82+96x^83+969x^84+1968x^85+564x^86+192x^87+1068x^88+2088x^89+540x^90+288x^91+1551x^92+2640x^93+636x^94+192x^95+933x^96+1236x^97+264x^98+111x^100+12x^104+9x^108

The gray image is a linear code over GF(4) with n=120, k=7 and d=80.
This code was found by Heurico 1.16 in 0.375 seconds.