The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+62x^33+122x^34+436x^35+298x^36+920x^37+475x^38+912x^39+253x^40+416x^41+101x^42+60x^43+21x^44+8x^45+5x^46+2x^48+2x^49+1x^50+1x^52

The gray image is a code over GF(2) with n=304, k=12 and d=132.
This code was found by Heurico 1.16 in 0.297 seconds.