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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+158x^78+552x^79+921x^80+1308x^81+1358x^82+1902x^83+1848x^84+2442x^85+2293x^86+2616x^87+2326x^88+2620x^89+2199x^90+2414x^91+1887x^92+1784x^93+1340x^94+970x^95+689x^96+494x^97+230x^98+236x^99+97x^100+52x^101+5x^102+14x^103+7x^104+2x^105+1x^106+2x^109

The gray image is a code over GF(2) with n=352, k=15 and d=156.
This code was found by Heurico 1.13 in 22.5 seconds.