The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+368x^37+770x^38+822x^39+700x^40+466x^41+401x^42+270x^43+144x^44+106x^45+28x^46+12x^47+3x^48+4x^49+1x^50

The gray image is a code over GF(2) with n=320, k=12 and d=148.
This code was found by Heurico 1.16 in 0.094 seconds.