The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+588x^107+804x^108+516x^109+1320x^110+2184x^111+2214x^112+1056x^113+2136x^114+3804x^115+3813x^116+1632x^117+3804x^118+5760x^119+4905x^120+1992x^121+4332x^122+6420x^123+5118x^124+1644x^125+3180x^126+3576x^127+2262x^128+792x^129+588x^130+708x^131+321x^132+48x^133+15x^136+3x^144

The gray image is a linear code over GF(4) with n=160, k=8 and d=107.
This code was found by Heurico 1.16 in 22.2 seconds.