The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+156x^42+28x^43+497x^44+252x^45+818x^46+740x^47+1610x^48+1240x^49+2092x^50+1588x^51+2075x^52+1312x^53+1588x^54+732x^55+745x^56+200x^57+400x^58+48x^59+163x^60+4x^61+66x^62+27x^64+1x^68+1x^72

The gray image is a code over GF(2) with n=204, k=14 and d=84.
This code was found by Heurico 1.16 in 10.8 seconds.