The generator matrix

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

generates a code of length 21 over F4[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+312x^57+576x^59+600x^60+504x^61+384x^63+63x^64+360x^65+576x^67+360x^68+360x^69

The gray image is a linear code over GF(4) with n=84, k=6 and d=57.
This code was found by Heurico 1.16 in 4.41 seconds.