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  1  X  1  1  1  X  1  1  1  1  X 2X+2  1 2X+2  1  X  X
 0  2  0 2X+2  0  0 2X+2 2X+2 2X 2X 2X+2  2  2  2  0 2X  0 2X+2 2X 2X+2  2  0  0 2X+2 2X+2 2X  0  2  2  0 2X  2  2 2X+2  2 2X+2 2X 2X+2 2X+2  0  2 2X+2 2X
 0  0  2 2X+2  0  2  2  0 2X 2X+2 2X+2  0 2X 2X+2 2X  2  0  2  2 2X  0 2X+2  0 2X+2 2X 2X+2 2X+2  0  0 2X 2X 2X  0 2X+2  2 2X+2 2X+2  2 2X  2 2X  2 2X+2
 0  0  0 2X  0  0 2X  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X
 0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  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+105x^38+8x^39+140x^40+128x^41+417x^42+496x^43+393x^44+128x^45+125x^46+8x^47+58x^48+23x^50+15x^52+2x^54+1x^72

The gray image is a code over GF(2) with n=344, k=11 and d=152.
This code was found by Heurico 1.16 in 1.36 seconds.