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

generates a code of length 71 over F4[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+33x^204+33x^208+66x^212+768x^213+78x^216+42x^220+3x^284

The gray image is a linear code over GF(4) with n=284, k=5 and d=204.
This code was found by Heurico 1.16 in 0.063 seconds.