The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+90x^37+578x^38+1630x^39+2617x^40+4200x^41+4332x^42+5754x^43+4895x^44+4092x^45+2340x^46+1348x^47+506x^48+250x^49+76x^50+34x^51+13x^52+6x^53+2x^54+2x^55+2x^57

The gray image is a code over GF(2) with n=344, k=15 and d=148.
This code was found by Heurico 1.16 in 6.13 seconds.