The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+300x^59+702x^60+1294x^61+1733x^62+2548x^63+3166x^64+3940x^65+4523x^66+5512x^67+5796x^68+6366x^69+5685x^70+5860x^71+4700x^72+4136x^73+3105x^74+2396x^75+1576x^76+960x^77+542x^78+378x^79+175x^80+64x^81+26x^82+28x^83+10x^84+8x^85+2x^87+2x^88+2x^90

The gray image is a code over GF(2) with n=276, k=16 and d=118.
This code was found by Heurico 1.13 in 65.1 seconds.