The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+152x^76+64x^77+312x^78+268x^79+660x^80+640x^81+748x^82+972x^83+1180x^84+1272x^85+1176x^86+1632x^87+1151x^88+1464x^89+1026x^90+960x^91+782x^92+616x^93+408x^94+244x^95+302x^96+40x^97+128x^98+20x^99+80x^100+40x^102+25x^104+2x^106+14x^108+5x^112

The gray image is a code over GF(2) with n=348, k=14 and d=152.
This code was found by Heurico 1.16 in 22.8 seconds.