The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+60x^77+114x^78+178x^79+276x^80+266x^81+374x^82+370x^83+455x^84+462x^85+591x^86+750x^87+624x^88+732x^89+542x^90+470x^91+459x^92+352x^93+266x^94+190x^95+154x^96+130x^97+108x^98+70x^99+59x^100+38x^101+43x^102+18x^103+16x^104+8x^105+8x^106+2x^107+3x^108+1x^110+1x^112+1x^126

The gray image is a code over GF(2) with n=352, k=13 and d=154.
This code was found by Heurico 1.16 in 15.4 seconds.