The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+76x^37+110x^38+76x^39+65x^40+48x^41+49x^42+24x^43+20x^44+20x^45+8x^46+12x^47+1x^48+1x^50+1x^56

The gray image is a code over GF(2) with n=160, k=9 and d=74.
This code was found by Heurico 1.13 in 0.016 seconds.