The generator matrix

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

generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+645x^44+492x^45+660x^46+1824x^47+3768x^48+3624x^49+3120x^50+5328x^51+15282x^52+14136x^53+9720x^54+18000x^55+38430x^56+27312x^57+14640x^58+23664x^59+38334x^60+21180x^61+8724x^62+6480x^63+5835x^64+840x^65+66x^68+30x^72+9x^76

The gray image is a linear code over GF(4) with n=76, k=9 and d=44.
This code was found by Heurico 1.16 in 41.5 seconds.