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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+156x^76+104x^78+8x^79+452x^80+56x^81+328x^82+176x^83+771x^84+336x^85+788x^86+448x^87+1004x^88+448x^89+864x^90+336x^91+688x^92+176x^93+352x^94+56x^95+319x^96+8x^97+120x^98+117x^100+4x^102+40x^104+24x^108+8x^112+3x^116+1x^132

The gray image is a code over GF(2) with n=352, k=13 and d=152.
This code was found by Heurico 1.16 in 30.9 seconds.