The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+124x^40+2x^48+1x^64

The gray image is a code over GF(2) with n=160, k=7 and d=80.
This code was found by an older version of Heurico in 0 seconds.