The generator matrix

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

generates a code of length 21 over F4[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+336x^54+1239x^56+1332x^58+1860x^60+2628x^62+3510x^64+2844x^66+2028x^68+540x^70+57x^72+9x^80

The gray image is a linear code over GF(4) with n=84, k=7 and d=54.
This code was found by Heurico 1.16 in 4.13 seconds.