The generator matrix

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

generates a code of length 26 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+96x^60+60x^62+24x^63+330x^64+312x^66+360x^67+456x^68+2436x^70+2160x^71+504x^72+7440x^74+6480x^75+543x^76+14340x^78+9720x^79+696x^80+11064x^82+5832x^83+681x^84+1212x^86+468x^88+225x^92+81x^96+15x^100

The gray image is a linear code over GF(4) with n=104, k=8 and d=60.
This code was found by Heurico 1.16 in 6.66 seconds.