The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+90x^116+396x^117+60x^120+252x^121+102x^124+36x^125+84x^129+3x^144

The gray image is a linear code over GF(4) with n=160, k=5 and d=116.
This code was found by Heurico 1.16 in 0.391 seconds.