The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  0  0  1  1  1  1  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1 a^2*X+1 a^2*X+a^2  1  1  0  a  0 a^2*X+1  X
 0  0 a^2*X  0  0  X  0 a*X a*X a^2*X a^2*X a*X a*X  0 a^2*X a^2*X a^2*X a*X a^2*X
 0  0  0  X  0 a^2*X a*X a^2*X  0 a^2*X a^2*X a^2*X a*X a^2*X  X  0  0 a*X  0
 0  0  0  0 a^2*X  X  X a^2*X a*X a*X  X  0 a*X a^2*X a*X  X a^2*X  0  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+54x^44+12x^45+60x^46+258x^48+336x^49+240x^50+1032x^52+1224x^53+840x^54+2745x^56+2640x^57+1200x^58+2805x^60+1932x^61+732x^62+147x^64+90x^68+33x^72+3x^76

The gray image is a linear code over GF(4) with n=76, k=7 and d=44.
This code was found by Heurico 1.16 in 0.291 seconds.