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.