The generator matrix

 1  0  0  1  1  1  1  1  1  1  0  1  1  1  1  1 a^2*X a*X  1  1  1
 0  1  0  1  a a^2*X a^2*X+a^2 a^2*X+1 a^2*X  0  1  a  X  0 X+a^2 a^2*X+a  1  1 a^2*X+1  X a^2*X+1
 0  0  1 a^2  a  1  X  0 a^2  a  a  0 a^2*X+1 a^2*X  0 a^2 a^2*X+a^2  a X+a a^2*X X+a
 0  0  0  X  0  0  X a^2*X  0 a^2*X  X  X  X a^2*X  X a^2*X  X a^2*X a*X a^2*X a^2*X
 0  0  0  0  X a*X a^2*X a*X a^2*X a^2*X a^2*X  X  X  X  0  0 a*X a^2*X  X  0  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+456x^51+480x^52+156x^53+144x^54+2196x^55+1725x^56+336x^57+1296x^58+6816x^59+5040x^60+936x^61+3888x^62+12888x^63+7449x^64+1104x^65+3888x^66+10296x^67+4551x^68+540x^69+1140x^71+129x^72+54x^76+24x^80+3x^84

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 6.86 seconds.