The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  a a^2  0  1 a^2*X+a a^2*X+1 a^2*X+a^2 a^2*X+a a^2*X a^2*X+a X+a a*X+a^2 a^2*X+a^2 a^2  0
 0  0  1 a^2  a  1  a  1 a^2  a X+a  1 X+1 X+1 a^2*X+a a^2*X+a  X  X  X
 0  0  0  X  0  X  0  X a^2*X a^2*X a^2*X  0 a^2*X  0  X  X a^2*X  0 a*X
 0  0  0  0  X a^2*X a*X  X  0 a^2*X a*X a*X  X  0 a*X  X  X a^2*X a^2*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+126x^44+24x^45+288x^46+624x^47+834x^48+288x^49+1680x^50+1728x^51+3234x^52+1296x^53+4752x^54+6048x^55+8676x^56+2592x^57+7344x^58+7872x^59+8544x^60+1944x^61+4368x^62+2160x^63+993x^64+90x^68+24x^72+6x^76

The gray image is a linear code over GF(4) with n=76, k=8 and d=44.
This code was found by Heurico 1.16 in 3.77 seconds.