The generator matrix

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

generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+442x^37+688x^38+778x^39+681x^40+550x^41+419x^42+254x^43+108x^44+136x^45+20x^46+16x^47+2x^48+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.