The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  1  1
 0  1  0  1  a a+1 (a+1)X (a+1)X+1 (a+1)X+a+1 (a+1)X+a+1 (a+1)X  X aX X+a  1 a+1 a+1 aX+a (a+1)X
 0  0  1 a+1  a  1  1  0  a  0 a+1 (a+1)X+a (a+1)X+1 X+a X+a+1 X+a a+1 X+a+1  1
 0  0  0  X  0  X  0 aX (a+1)X  X aX aX  X (a+1)X (a+1)X  X  0 (a+1)X (a+1)X
 0  0  0  0  X (a+1)X (a+1)X  0 (a+1)X  X aX  X  0 aX  0  X  X (a+1)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+177x^44+48x^45+228x^46+432x^47+1032x^48+576x^49+1008x^50+1296x^51+4236x^52+2592x^53+3288x^54+3888x^55+10878x^56+5184x^57+4848x^58+5040x^59+10848x^60+3888x^61+2916x^62+1632x^63+1371x^64+96x^68+30x^72+3x^76

The gray image is a linear code over GF(4) with n=76, k=8 and d=44.
This code was found by Heurico 1.16 in 3.89 seconds.