The generator matrix

 1  0  0  1  1  1 X+2  1  1  X  1  2  1  2  1  1  X  X  1  1  1  2 X+2  0  1  1  1  1  1  X X+2  1  0  X X+2  0  1  1  1  1 X+2  1  1  1  1  1  1  0  1 X+2  1  0  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  1
 0  1  0  0  1 X+3  1 X+2 X+3  1  3  1  X  X  X  0  X  1  3  3 X+2  1  0  1  1 X+1 X+3  X  2  1  0  1 X+2  1  1  1  X  2 X+1 X+1  1  0  X X+3 X+1 X+3 X+2  1  0  1  2  0  1 X+2  2  1  1 X+1  1  1  2  1 X+2  X  1  X  1 X+1 X+2
 0  0  1  1 X+1  0 X+3  1 X+3 X+2  X  3  X  1 X+1 X+2  1  1  3  2  2  0  1 X+3  X  0  3 X+1  X  0  1  3  1 X+2 X+1 X+2  3 X+1  3 X+2  0  2 X+1 X+1  0  0  3 X+1 X+2  0  X  1 X+1  X  1  X  3 X+1 X+3  X  3  0  1  3  2  1  1 X+2 X+3
 0  0  0  X  X X+2  0 X+2 X+2  0 X+2  2  2  0  X  2  2  2  X X+2 X+2  X  2  X  0  0  0  0 X+2 X+2 X+2  2  X X+2  X  X  0 X+2  X  0  X  X  X X+2  0 X+2 X+2  X  2  2 X+2 X+2  X X+2  2  0 X+2  2  2  0  0  X  2  0 X+2  2  0  X  2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  2  2  0  0  0  2  0  2  2  0  0  0  2  0  2  0  2  0  2  0  0  2  2  0  0  2  2  2  0  0  2  0  2  2  2  2  0  2  0  2  0  0  0  0  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  0  2  0  0  0  2  2  2  2  0  2  0  2  2  2  2  2  2  2  2  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  0  0
 0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  0  2  0  2  2  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  2  0  0  2  0  2  2  2  0  2  0  0  2  0  2  0  2  2  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 60.

Homogenous weight enumerator: w(x)=1x^0+118x^60+250x^61+604x^62+534x^63+1022x^64+920x^65+1215x^66+1278x^67+1668x^68+1358x^69+1617x^70+1186x^71+1337x^72+866x^73+1000x^74+496x^75+421x^76+160x^77+139x^78+70x^79+32x^80+30x^81+28x^82+18x^83+5x^84+4x^86+2x^87+4x^88+1x^90

The gray image is a code over GF(2) with n=276, k=14 and d=120.
This code was found by Heurico 1.16 in 13.5 seconds.