The generator matrix

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

generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+120x^51+36x^52+864x^53+480x^54+360x^55+108x^56+576x^57+72x^59+108x^60+864x^61+288x^62+216x^63+3x^64

The gray image is a linear code over GF(4) with n=76, k=6 and d=51.
This code was found by Heurico 1.16 in 0.015 seconds.