The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+550x^44+1796x^46+2690x^48+3256x^50+3120x^52+2816x^54+1440x^56+552x^58+122x^60+28x^62+13x^64

The gray image is a code over GF(2) with n=204, k=14 and d=88.
This code was found by Heurico 1.13 in 1070 seconds.