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

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+160x^76+4x^77+274x^78+56x^79+549x^80+136x^81+544x^82+256x^83+862x^84+360x^85+748x^86+400x^87+839x^88+400x^89+756x^90+256x^91+522x^92+116x^93+346x^94+56x^95+272x^96+8x^97+120x^98+76x^100+24x^102+33x^104+4x^106+10x^108+2x^112+2x^116

The gray image is a code over GF(2) with n=348, k=13 and d=152.
This code was found by Heurico 1.16 in 9.49 seconds.