The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+72x^38+200x^39+221x^40+608x^41+480x^42+944x^43+480x^44+608x^45+210x^46+200x^47+63x^48+4x^54+3x^56+2x^62

The gray image is a code over GF(2) with n=344, k=12 and d=152.
This code was found by Heurico 1.16 in 0.172 seconds.