The generator matrix

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

generates a code of length 21 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+276x^51+186x^52+312x^53+1140x^54+1512x^55+1236x^56+1272x^57+3408x^58+3792x^59+3117x^60+3288x^61+7464x^62+7560x^63+6009x^64+4488x^65+7920x^66+6012x^67+2712x^68+1392x^69+1572x^70+816x^71+36x^72+9x^76+6x^80

The gray image is a linear code over GF(4) with n=84, k=8 and d=51.
This code was found by Heurico 1.16 in 4.14 seconds.