The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+1020x^108+1344x^112+696x^116+720x^120+300x^124+15x^128

The gray image is a linear code over GF(4) with n=152, k=6 and d=108.
This code was found by Heurico 1.16 in 105 seconds.