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 1 1 1 1 1 1 1 1 1 1 X X 1 2 X 2 X X X 1 1 2 X 1
0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 X X X+2 X+2 X+2 X X 2 2 X 2 0 X X 0 X 2 X+2 2 0 2 0 X 0 X X+2 X+2 2 0 0 2 0 0
0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X 0 X+2 X+2 X X+2 2 2 X+2 0 X 2 X+2 0 X X+2 2 X+2 X 2 2 X+2 X+2 0 X+2 X+2 2 X+2 X+2 0 2 X X 0
0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 X+2 2 X+2 2 X+2 0 2 X+2 X 2 2 X+2 X 2 0 0 0 X+2 X+2 X X+2 X X+2 X+2 X+2 0 X+2 0 X X 2 X 0
0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 2 0 X+2 0 X+2 0 X+2 X+2 0 X X+2 2 2 2 X+2 X+2 X+2 0 0 X+2 0 X+2 X+2 X X+2 X X 0 X X+2 X 2 0
0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X+2 2 X+2 X 0 X 2 X+2 0 2 0 X+2 2 X+2 2 X 0 X X X 0 X X 2 0 X X+2 X+2 2 0 2 2 0
0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 0 2 2 0 2 2 2 0 2 0 0 0 2 0 0 0 0 0 0 2 2 2 0 2 0 2 0 2 0
generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+62x^40+92x^41+195x^42+268x^43+348x^44+412x^45+536x^46+774x^47+1096x^48+1540x^49+1874x^50+2008x^51+1865x^52+1552x^53+1085x^54+828x^55+549x^56+412x^57+314x^58+172x^59+157x^60+84x^61+87x^62+46x^63+16x^64+4x^65+4x^66+2x^68+1x^82
The gray image is a code over GF(2) with n=204, k=14 and d=80.
This code was found by Heurico 1.16 in 14.2 seconds.