The generator matrix

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

generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+135x^40+297x^44+336x^45+636x^48+2880x^49+2229x^52+10080x^53+5820x^56+19008x^57+6105x^60+16848x^61+735x^64+267x^68+129x^72+30x^76

The gray image is a linear code over GF(4) with n=76, k=8 and d=40.
This code was found by Heurico 1.16 in 3.9 seconds.