The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+85x^36+208x^37+205x^38+596x^39+644x^40+796x^41+607x^42+472x^43+134x^44+168x^45+73x^46+52x^47+31x^48+12x^49+8x^50+1x^52+2x^54+1x^66

The gray image is a code over GF(2) with n=328, k=12 and d=144.
This code was found by Heurico 1.16 in 0.219 seconds.