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 aX aX  1  1
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a  X (a+1)X+a+1  1 (a+1)X+1 X+a aX+a+1  1  X  1 X+a aX+a+1  1  0  X aX aX (a+1)X+1 aX+1 aX+1 aX+1  a X+a aX+a (a+1)X+a+1  1 aX+a+1  1  1 X+a+1 aX+a
 0  0 (a+1)X  X aX  X  0 (a+1)X aX (a+1)X (a+1)X  X aX  0 aX (a+1)X aX  0  X  X aX  X  0 (a+1)X aX (a+1)X  X  0  0 (a+1)X  X  0 aX (a+1)X  X  0 aX aX

generates a code of length 38 over F4[X,sigma]/(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 0.232 seconds.