The generator matrix

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

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+100x^37+49x^38+128x^39+27x^40+64x^41+46x^42+60x^43+2x^44+28x^45+1x^46+4x^51+2x^56

The gray image is a code over GF(2) with n=160, k=9 and d=74.
This code was found by Heurico 1.16 in 0.0326 seconds.