The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+39x^104+96x^105+312x^107+243x^108+360x^109+396x^111+195x^112+360x^113+348x^115+330x^116+504x^117+324x^119+171x^120+216x^121+156x^123+15x^124+12x^128+12x^132+6x^136

The gray image is a linear code over GF(4) with n=152, k=6 and d=104.
This code was found by Heurico 1.16 in 0.054 seconds.