The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+228x^103+684x^104+348x^105+732x^106+3156x^107+3066x^108+2004x^109+2628x^110+8028x^111+7152x^112+4884x^113+6264x^114+17352x^115+13068x^116+9612x^117+10296x^118+27708x^119+20247x^120+13236x^121+12924x^122+29028x^123+17223x^124+9948x^125+8196x^126+15972x^127+8820x^128+2844x^129+1968x^130+2976x^131+1302x^132+132x^133+60x^136+33x^140+9x^144+12x^148+3x^152

The gray image is a linear code over GF(4) with n=160, k=9 and d=103.
This code was found by Heurico 1.16 in 131 seconds.