The generator matrix

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

generates a code of length 21 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+66x^44+246x^48+192x^51+888x^52+2304x^55+1860x^56+10368x^59+3174x^60+20736x^63+4623x^64+15552x^67+4662x^68+564x^72+216x^76+66x^80+18x^84

The gray image is a linear code over GF(4) with n=84, k=8 and d=44.
This code was found by Heurico 1.16 in 4.4 seconds.