The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  X  1  X  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X  X a*X  0 a^2*X a*X  X a*X  0  X  0 a^2*X a*X  X a^2*X a*X  0  0 a*X a*X  X a^2*X  X a^2*X a^2*X  0 a^2*X a*X a*X a*X  X  X  0 a*X  0  X  0 a*X a*X  0  X a*X  X a*X  X a^2*X  0  0  X a*X  X a^2*X  X  0  X  X  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X a^2*X a^2*X  0  X a^2*X  0 a^2*X  0 a*X a*X a*X a*X a^2*X  0 a^2*X a^2*X  0  0 a^2*X  X  X  0 a*X  0  X a*X  X  X a*X  X  X  0  0 a*X a*X a*X  X a*X  0 a^2*X a^2*X  0 a^2*X a^2*X a*X a^2*X a*X  0 a*X a^2*X a*X  X a^2*X a^2*X  0
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  X  X a^2*X a^2*X a^2*X a*X  0 a^2*X a^2*X  0  X a*X  0 a^2*X  0 a*X  X  X a*X  0 a*X  0  X a^2*X  0 a^2*X  0 a*X  X a*X a*X  X a*X a^2*X  X  X a^2*X a^2*X  0  X a^2*X  X  0  X  X a^2*X a^2*X a^2*X  X  X a^2*X  0 a^2*X  X a^2*X a*X a^2*X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X  X a*X a^2*X a^2*X a*X  0 a*X  X a*X a*X  0  0 a^2*X a^2*X a^2*X a*X  X  0  0  X a*X a*X  X  0 a*X  X a^2*X a^2*X  X a^2*X a^2*X a^2*X  X a^2*X a*X  X a^2*X  0 a^2*X a*X a*X a*X a^2*X  X a*X  0  0  0  0 a^2*X  0 a*X  X  X a*X  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+93x^204+12x^207+207x^208+144x^211+162x^212+648x^215+132x^216+1296x^219+108x^220+972x^223+72x^224+39x^228+60x^232+24x^236+42x^240+36x^244+21x^248+15x^252+6x^256+3x^264+3x^276

The gray image is a linear code over GF(4) with n=292, k=6 and d=204.
This code was found by Heurico 1.16 in 0.265 seconds.