The generator matrix

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

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+97x^78+210x^79+465x^80+474x^81+829x^82+852x^83+1154x^84+1016x^85+1401x^86+1044x^87+1452x^88+1196x^89+1439x^90+944x^91+1079x^92+708x^93+675x^94+450x^95+366x^96+162x^97+139x^98+76x^99+77x^100+16x^101+19x^102+8x^103+10x^104+8x^105+9x^106+1x^108+4x^109+2x^112+1x^116

The gray image is a code over GF(2) with n=352, k=14 and d=156.
This code was found by Heurico 1.16 in 19 seconds.