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

generates a code of length 37 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+54x^104+48x^105+78x^108+288x^109+84x^112+432x^113+12x^120+12x^124+3x^128+6x^136+6x^140

The gray image is a linear code over GF(4) with n=148, k=5 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.