The generator matrix

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

generates a code of length 19 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+78x^40+303x^44+192x^45+639x^48+2304x^49+2247x^52+10368x^53+5859x^56+20736x^57+6201x^60+15552x^61+684x^64+237x^68+99x^72+36x^76

The gray image is a linear code over GF(4) with n=76, k=8 and d=40.
This code was found by Heurico 1.16 in 3.89 seconds.