The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+201x^58+509x^60+4x^61+845x^62+100x^63+1151x^64+456x^65+1545x^66+956x^67+1935x^68+1128x^69+1954x^70+860x^71+1611x^72+456x^73+1053x^74+132x^75+699x^76+4x^77+433x^78+212x^80+103x^82+25x^84+8x^86+2x^90+1x^104

The gray image is a code over GF(2) with n=276, k=14 and d=116.
This code was found by Heurico 1.16 in 23.2 seconds.