The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+208x^35+365x^36+476x^37+346x^38+572x^39+404x^40+452x^41+361x^42+316x^43+225x^44+180x^45+76x^46+84x^47+13x^48+12x^49+1x^50+4x^51

The gray image is a code over GF(2) with n=160, k=12 and d=70.
This code was found by Heurico 1.11 in 0.177 seconds.