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  X  0  1  1  2  X  0  X  X  X  1  2  2  1  1  1  1  X  0  X  1  0  0  1  X  1  1  X  X  1  X  1  X
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  X  2 X+2  0  X  X  0  2  2 X+2  2  X X+2  0  X  2  0  2  0  0 X+2  X  0 X+2  X  2  2  X X+2  0  X  2  0  X  2  2  X X+2  X  0  2  X  X X+2  X  0  2  X  0  X X+2  0  2 X+2  X  0
 0  0  X  0  0  0  X X+2  X  2  X X+2  0  0  X  X  2 X+2 X+2 X+2  0 X+2 X+2 X+2 X+2  2  2 X+2 X+2  2  0  2  2 X+2  0  2  2  0  2  X  0 X+2  X  0  0 X+2 X+2  X  X  2  2  X  2  X  2  2  0  X  X  2 X+2 X+2 X+2 X+2  2  X  0  0 X+2
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  0  X  0  X  X X+2  2  0 X+2  2  0  2  2  2  X  2  X  2 X+2  X  0 X+2 X+2  2  2 X+2 X+2  X  X  2  2 X+2  0 X+2  2  X  X  X  0  0  2 X+2  0  0  2  X X+2  X  0  X  2  0  2  2  2  0
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2 X+2  X  0  X  2  2  0  2  0  X  X  0  X  2  2  0 X+2  2 X+2  X  2 X+2  2  0 X+2  X  2  0  0 X+2  0  2  2 X+2  0  X X+2  0  0 X+2  X  0  2  0  0  X  X X+2  2 X+2 X+2  2  2 X+2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  0  2  2  0  2  0  0  2  2  0  2  0  2  2  0  2  2  0  2  2  0  0  2  0  2  0  0  2  0  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  0  2  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  2  0  0  0  2  2  2  0  2  0  0  0  0  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  0  0  2  2  2  2  0  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+74x^59+118x^60+198x^61+317x^62+314x^63+365x^64+470x^65+643x^66+652x^67+622x^68+690x^69+771x^70+704x^71+478x^72+494x^73+366x^74+212x^75+206x^76+156x^77+105x^78+76x^79+58x^80+36x^81+30x^82+14x^83+6x^84+4x^85+7x^86+2x^87+2x^88+1x^98

The gray image is a code over GF(2) with n=276, k=13 and d=118.
This code was found by Heurico 1.16 in 6.43 seconds.