The generator matrix

 1  0  0  1  1  1  2  0  1  1  2  0  1  1  X X+2  1  0  1  1  1  2  1  X  1  1  X  1 X+2  0  1 X+2  1 X+2  1  X X+2  1  2  2
 0  1  0  0  3  3  1 X+2  2  1  1  1  2  1  X  2  2  1  3 X+1  2  1  3 X+2 X+3  X  1 X+3  1  1  2  1 X+2  1 X+3  1  1  X X+2  1
 0  0  1 X+1 X+3  2 X+3  1  X  3  1  X  1 X+2  1  1 X+3  2  1  0  2 X+3  X  1 X+1  3  0  X  1  1  X X+2  0 X+2  X X+1  0  X  1 X+2
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  2  2  2  0  0  2  0  2  0  2  0  2  0  0  0  2  0  2  2  2  0  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+228x^37+136x^38+236x^39+26x^40+140x^41+64x^42+64x^43+68x^45+24x^46+20x^47+5x^48+12x^49

The gray image is a code over GF(2) with n=160, k=10 and d=74.
This code was found by Heurico 1.16 in 15.5 seconds.