The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+336x^49+973x^50+1604x^51+2017x^52+2290x^53+2446x^54+2218x^55+1796x^56+1234x^57+750x^58+384x^59+163x^60+102x^61+30x^62+18x^63+13x^64+6x^65+1x^66+2x^68

The gray image is a code over GF(2) with n=432, k=14 and d=196.
This code was found by Heurico 1.16 in 2.19 seconds.