The generator matrix

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

generates a code of length 25 over F4[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+384x^69+384x^70+216x^71+261x^72+588x^73+432x^74+144x^75+27x^76+264x^77+336x^78+216x^79+150x^80+492x^81+192x^82+9x^84

The gray image is a linear code over GF(4) with n=100, k=6 and d=69.
This code was found by Heurico 1.16 in 0.125 seconds.