The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+42x^32+72x^33+151x^34+168x^35+244x^36+314x^37+374x^38+476x^39+466x^40+482x^41+367x^42+324x^43+208x^44+126x^45+104x^46+52x^47+59x^48+30x^49+25x^50+4x^51+4x^52+2x^54+1x^58

The gray image is a code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.691 seconds.