The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+84x^109+216x^110+27x^112+180x^113+216x^114+18x^116+60x^117+72x^118+12x^120+60x^121+72x^122+6x^124

The gray image is a linear code over GF(4) with n=152, k=5 and d=109.
This code was found by Heurico 1.16 in 0.469 seconds.