The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  1  1  2  X  X  X  0  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2  X X+3  1  1  1  0 X+2  X  0  2 X+2 X+2 X+1 X+3  3  3  0  2  X  X  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  2  0  2  0  0

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+56x^39+13x^40+32x^41+8x^42+8x^43+2x^44+1x^50+1x^58

The gray image is a code over GF(2) with n=160, k=7 and d=76.
This code was found by Heurico 1.13 in 0.016 seconds.