The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+37x^44+94x^45+292x^46+352x^47+478x^48+768x^49+929x^50+1270x^51+1532x^52+1634x^53+1664x^54+1666x^55+1519x^56+1264x^57+987x^58+682x^59+456x^60+296x^61+197x^62+114x^63+62x^64+38x^65+24x^66+8x^67+11x^68+3x^70+4x^71+2x^73

The gray image is a code over GF(2) with n=216, k=14 and d=88.
This code was found by Heurico 1.16 in 11.7 seconds.