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

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+1116x^107+624x^108+4464x^111+1971x^112+8520x^115+3348x^116+12288x^119+3888x^120+13836x^123+4296x^124+7536x^127+1881x^128+1392x^131+372x^132+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 31 seconds.