The generator matrix

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

generates a code of length 26 over F4[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+288x^70+141x^72+696x^74+372x^76+984x^78+444x^80+936x^82+168x^86+48x^88+12x^92+3x^96+3x^104

The gray image is a linear code over GF(4) with n=104, k=6 and d=70.
This code was found by Heurico 1.16 in 1.56 seconds.