The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1 a^2*X  1  1  1  X  1  1  1
 0  1  0  0  X  1 X+1  1 a*X  1 a^2*X+a X+a^2 a*X  1 a^2*X+1 a^2*X+a^2 a^2*X+1 a*X a*X+1 a^2  0
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a a^2*X+a^2  X a*X+a a*X+a  1 a*X+a a*X+1  1 a^2 X+a^2  0
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X X+a a^2*X+a^2 a^2*X a^2*X+1 a*X+a^2 a*X+a a*X+a a*X+1  0 a^2 a^2*X

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

Homogenous weight enumerator: w(x)=1x^0+252x^51+234x^52+372x^53+1116x^54+1344x^55+1221x^56+1512x^57+3144x^58+3552x^59+3732x^60+3744x^61+6768x^62+7032x^63+6555x^64+4920x^65+7512x^66+5508x^67+3054x^68+1740x^69+1428x^70+744x^71+33x^72+12x^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 4.06 seconds.