The generator matrix

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

generates a code of length 26 over F4[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+384x^66+492x^67+546x^68+1140x^69+1812x^70+1716x^71+1974x^72+2628x^73+3732x^74+3540x^75+4299x^76+4572x^77+6732x^78+5556x^79+5619x^80+5292x^81+6108x^82+3504x^83+2367x^84+1728x^85+1200x^86+552x^87+24x^88+9x^92+6x^96+3x^100

The gray image is a linear code over GF(4) with n=104, k=8 and d=66.
This code was found by Heurico 1.16 in 5.91 seconds.