The generator matrix

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

generates a code of length 73 over F4[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+1680x^204+6582x^208+10068x^212+10944x^216+12396x^220+11601x^224+8076x^228+3336x^232+804x^236+48x^240

The gray image is a linear code over GF(4) with n=292, k=8 and d=204.
This code was found by Heurico 1.16 in 50.4 seconds.