The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+174x^37+367x^38+514x^39+693x^40+714x^41+656x^42+476x^43+268x^44+148x^45+46x^46+12x^47+13x^48+2x^49+4x^51+2x^53+3x^54+2x^55+1x^56

The gray image is a code over GF(2) with n=328, k=12 and d=148.
This code was found by Heurico 1.16 in 2.34 seconds.