The generator matrix

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

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+110x^59+152x^60+346x^61+367x^62+818x^63+654x^64+1238x^65+872x^66+1636x^67+1072x^68+1932x^69+1078x^70+1764x^71+826x^72+1254x^73+612x^74+648x^75+296x^76+296x^77+113x^78+120x^79+55x^80+52x^81+26x^82+22x^83+16x^84+2x^85+2x^86+2x^87+2x^90

The gray image is a code over GF(2) with n=276, k=14 and d=118.
This code was found by Heurico 1.16 in 35.7 seconds.