The generator matrix

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

generates a code of length 25 over F4[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+81x^56+306x^60+372x^64+462x^68+768x^69+561x^72+4608x^73+660x^76+6912x^77+699x^80+486x^84+342x^88+102x^92+24x^96

The gray image is a linear code over GF(4) with n=100, k=7 and d=56.
This code was found by Heurico 1.16 in 0.804 seconds.