The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+78x^60+408x^61+944x^62+1530x^63+2623x^64+3480x^65+5147x^66+5926x^67+7651x^68+9154x^69+10842x^70+10918x^71+12183x^72+11544x^73+11729x^74+9564x^75+8331x^76+5958x^77+4792x^78+3098x^79+2179x^80+1286x^81+809x^82+422x^83+188x^84+160x^85+64x^86+30x^87+14x^88+10x^89+7x^90+2x^94

The gray image is a code over GF(2) with n=288, k=17 and d=120.
This code was found by Heurico 1.13 in 335 seconds.