The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+189x^104+168x^105+132x^106+288x^107+1446x^108+768x^109+492x^110+996x^111+3669x^112+1440x^113+900x^114+2064x^115+6459x^116+2640x^117+1272x^118+3192x^119+9561x^120+3144x^121+1740x^122+3696x^123+8877x^124+2880x^125+1212x^126+1860x^127+4044x^128+1200x^129+396x^130+192x^131+435x^132+48x^133+54x^136+57x^140+18x^144+6x^148

The gray image is a linear code over GF(4) with n=160, k=8 and d=104.
This code was found by Heurico 1.16 in 10.6 seconds.