The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+312x^107+393x^108+288x^109+72x^110+384x^111+486x^112+348x^113+84x^114+216x^115+297x^116+144x^117+192x^119+351x^120+156x^121+36x^122+240x^123+66x^124+24x^125+6x^128

The gray image is a linear code over GF(4) with n=152, k=6 and d=107.
This code was found by Heurico 1.16 in 1.64 seconds.