The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+164x^77+524x^78+912x^79+1247x^80+1450x^81+1729x^82+2040x^83+2194x^84+2474x^85+2431x^86+2582x^87+2764x^88+2380x^89+2207x^90+1966x^91+1558x^92+1260x^93+1088x^94+690x^95+412x^96+344x^97+164x^98+82x^99+48x^100+20x^101+16x^102+16x^103+2x^105+2x^109+1x^110

The gray image is a code over GF(2) with n=348, k=15 and d=154.
This code was found by Heurico 1.13 in 22.3 seconds.