The generator matrix

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

generates a code of length 38 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+153x^100+1170x^104+1974x^108+4479x^112+5043x^116+3048x^120+357x^124+69x^128+48x^132+30x^136+9x^140+3x^144

The gray image is a linear code over GF(4) with n=152, k=7 and d=100.
This code was found by Heurico 1.16 in 0.759 seconds.