The generator matrix

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

generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+144x^53+360x^54+36x^56+96x^57+24x^60+144x^61+216x^62+3x^64

The gray image is a linear code over GF(4) with n=76, k=5 and d=53.
This code was found by Heurico 1.16 in 0.015 seconds.