The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X X 2 X 2 X 0 X 0 X 2 X 2 1 1 X X
0 X 0 X+2 0 X+2 0 X 2 X+2 2 X 2 X+2 2 X X+2 X X+2 X 0 2 X X X X X+2 X X+2 X X X X X 0 0 2 0
0 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0
0 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 0 2 2 2 0 0 2 2 0 0 2 0 2 2 0 0 2 2 0
generates a code of length 38 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+23x^36+76x^38+22x^40+4x^42+1x^48+1x^52
The gray image is a code over GF(2) with n=152, k=7 and d=72.
This code was found by Heurico 1.16 in 0.0206 seconds.