The generator matrix

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

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+69x^56+36x^58+252x^60+216x^62+48x^63+798x^64+636x^66+1344x^67+2619x^68+1872x^70+4896x^71+7074x^72+3996x^74+10560x^75+10413x^76+4056x^78+7728x^79+6504x^80+1476x^82+549x^84+285x^88+87x^92+21x^96

The gray image is a linear code over GF(4) with n=100, k=8 and d=56.
This code was found by Heurico 1.16 in 6.13 seconds.