The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+156x^112+108x^116+396x^120+324x^124+27x^128+12x^144

The gray image is a linear code over GF(4) with n=160, k=5 and d=112.
This code was found by Heurico 1.16 in 1.01e-007 seconds.