The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  0  1  1 X+2  1  1 X+2  0  X  1  1  0  1 X+2  X  1 X+2  1  0 X+2  2  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1  0  3  1 X+2 X+1  1  0 X+1  1 X+2  3  0 X+1  1  0  3  1  0 X+2  1  1  1  0 X+2  1  2  1  0  2  1  2  X  1  1  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  0  2  2  2  0  2  0  2  0  0  2  0  2  2  0  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  2  2  2  2  0  2  0  0  0  2  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  0  2  2  2  0  0  0  0  2  0  0  0  0  2  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  0  0  2  0  0  2  2  0  2  2  2  0  2  0  2  2  0  0  0  0  2  0  2  0  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  0  2  2  0  0  2  0  2  0  0  0  2  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  2  2  2  2  2  2  2  0  0  0  2  0  0  0  2  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  2  0  2  0  2  2  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  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+47x^40+32x^41+57x^42+86x^43+148x^44+138x^45+421x^46+262x^47+907x^48+348x^49+1466x^50+336x^51+1549x^52+320x^53+959x^54+256x^55+338x^56+164x^57+117x^58+74x^59+62x^60+22x^61+40x^62+10x^63+18x^64+8x^66+1x^68+3x^70+1x^72+1x^78

The gray image is a code over GF(2) with n=204, k=13 and d=80.
This code was found by Heurico 1.16 in 2.73 seconds.