The generator matrix

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

generates a code of length 41 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+210x^104+339x^108+465x^112+192x^114+468x^116+1728x^118+447x^120+5184x^122+513x^124+5184x^126+444x^128+438x^132+417x^136+213x^140+90x^144+42x^148+6x^152+3x^156

The gray image is a linear code over GF(4) with n=164, k=7 and d=104.
This code was found by Heurico 1.16 in 1.67 seconds.