The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2
 0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2
 0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  2
 0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+6x^38+30x^39+73x^40+9x^42+6x^44+1x^50+2x^55

The gray image is a code over GF(2) with n=160, k=7 and d=76.
This code was found by Heurico 1.16 in 0.019 seconds.