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

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+123x^36+16x^37+40x^38+128x^39+357x^40+736x^41+336x^42+128x^43+106x^44+16x^45+8x^46+41x^48+11x^52+1x^72

The gray image is a code over GF(2) with n=328, k=11 and d=144.
This code was found by Heurico 1.16 in 2.59 seconds.