The generator matrix

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

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+675x^44+384x^45+936x^46+1344x^47+4068x^48+2964x^49+5280x^50+3696x^51+15099x^52+12384x^53+15792x^54+11952x^55+38046x^56+26856x^57+25632x^58+14928x^59+38295x^60+18240x^61+13800x^62+4944x^63+6111x^64+612x^65+69x^68+30x^72+6x^76

The gray image is a linear code over GF(4) with n=76, k=9 and d=44.
This code was found by Heurico 1.16 in 39.6 seconds.