The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+108x^113+420x^114+660x^115+24x^116+204x^117+612x^118+432x^119+18x^120+72x^121+240x^122+312x^123+9x^124+108x^125+324x^126+192x^127+84x^129+132x^130+132x^131+3x^132+9x^136

The gray image is a linear code over GF(4) with n=160, k=6 and d=113.
This code was found by Heurico 1.16 in 0.11 seconds.