The generator matrix

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

generates a code of length 19 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+60x^44+48x^46+243x^48+384x^49+288x^50+1017x^52+1152x^53+768x^54+2799x^56+2688x^57+1248x^58+2781x^60+1920x^61+720x^62+144x^64+75x^68+45x^72+3x^76

The gray image is a linear code over GF(4) with n=76, k=7 and d=44.
This code was found by Heurico 1.16 in 0.295 seconds.