The generator matrix

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

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+243x^104+204x^106+312x^107+732x^108+312x^110+672x^111+1152x^112+696x^114+1872x^115+1797x^116+912x^118+2208x^119+1929x^120+732x^122+1080x^123+960x^124+216x^126+240x^128+36x^132+36x^136+24x^140+15x^144+3x^148

The gray image is a linear code over GF(4) with n=156, k=7 and d=104.
This code was found by Heurico 1.16 in 1.68 seconds.