The generator matrix

 1  0  0  1  1  1  1 (a+1)X  1  1  1  1  X  1  1  1 aX  1  1  1  1  1  1 aX  1
 0  1  0 (a+1)X  X (a+1)X+1  1  1 aX+1 X+a  a (a+1)X+a  1 aX X+1 a+1  1 (a+1)X+a+1 X+a+1  0 (a+1)X+a aX+1  a  1 (a+1)X+1
 0  0  1  1 (a+1)X+a  a X+1 X+a+1 X+a+1 (a+1)X aX+a a+1  1 (a+1)X+a+1  X (a+1)X+1  a aX+a+1 X+a aX aX+1 aX  0 X+a X+a+1

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

Homogenous weight enumerator: w(x)=1x^0+372x^69+360x^70+216x^71+261x^72+624x^73+504x^74+144x^75+27x^76+228x^77+264x^78+216x^79+150x^80+504x^81+216x^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 0.031 seconds.