The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  1  2  X  1  0  1  1  1  X  1 X+2  1  2  1  1  X  1 X+2  0  1  1  1  1  X  1  1  1  2  1  1  0 X+2  0  1  1
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  0 X+1  1  2 X+3  1  1  X  1  3 X+2 X+3  1  1  1  X  1  0  1  X X+2  1  0  X X+1  X  3  2 X+2  1  X  1 X+3  X  1  1  1  2  0
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  2  0  0  X X+2 X+2  X  X  0  2  0  X  X  X  2 X+2  X  0 X+2  X  2  0  X  2  0 X+2  2 X+2 X+2  X  2  2  2 X+2  0  0  0  X  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  2  0  2  0  0  0  2  0  2  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2  2  0  2  0  2  2  2  0  0  2  0  0  0  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0  2  0  2  0  0  2  0  0  0  0  2  0  0  2  2  0  0  2  2  2  0  2  0  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  2  0  0  0  2  0  2  2  2  0  2  0  0  2  2  2  2  0  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  2  2  2  0  2  0  0  2  0  0  2  2  2  0  2  2  2  2  2  0  0  2  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  2  0  0  0  2  2  2  2  2  0  0  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+31x^40+38x^41+98x^42+160x^43+363x^44+262x^45+958x^46+462x^47+1905x^48+720x^49+2812x^50+792x^51+2793x^52+732x^53+1901x^54+500x^55+935x^56+262x^57+342x^58+120x^59+94x^60+30x^61+28x^62+14x^63+14x^64+4x^65+4x^66+5x^68+1x^70+2x^72+1x^76

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 10.3 seconds.