The generator matrix

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

generates a code of length 25 over F4[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+141x^64+234x^68+924x^72+2406x^76+156x^80+102x^84+84x^88+42x^92+6x^96

The gray image is a linear code over GF(4) with n=100, k=6 and d=64.
This code was found by Heurico 1.16 in 5.79 seconds.