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  X  0  1  1  X  1  0  1  1  X  1  1  0  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  0  1  X  1  X  X  1  2  X  1  1  1  1  X  1  1  0  0  1  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  X  0  2  2 X+2 X+2  0  0 X+2  X  2 X+2  0  X X+2  X  X  2 X+2  0  X X+2  0 X+2  2 X+2  X X+2  2  0  X  X  0  2  0  0 X+2  X  0  2  0 X+2  X  2  2 X+2  X X+2  X X+2  2  X  X  X  X  X X+2 X+2  X  X X+2 X+2 X+2  X X+2 X+2 X+2  X  X  X  X X+2  0  0
 0  0  2  0  0  0  0  0  0  0  2  0  2  2  2  0  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  2  0  2  0  0  2  2  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  2  0  0  2  0  2  2  0  2  2  0  2  2  2  2  0  2  2  2  0  0  2  2  0  2  2  0  2  2  0  2  2  0  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  2  0  2  2  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  0  2  2  0  0  2  0  0  2  2  0  2  0  2  0  0  0  0  2  0  2  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  2  0  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  2  2  0  2  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  0  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  2  2  0  2  2  0  2  2  2  2  0  2  0  2  2  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  2  0  2  0  0  0  2  2  2  2  0  2  2  2  0  0  2  2  2  2  0  2  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  2  0  2  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  2  2  0  0  2  2  2  0  0  0  0  0  2  2  0  2  0  2  2  0  0  2  2  2  0  0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  2  0  0  2  0  2  0  2  0  0  0  0  2  2  2  0  2  0  2  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 76.

Homogenous weight enumerator: w(x)=1x^0+55x^76+74x^78+8x^79+213x^80+56x^81+138x^82+176x^83+302x^84+336x^85+172x^86+448x^87+210x^88+448x^89+172x^90+336x^91+249x^92+176x^93+138x^94+56x^95+162x^96+8x^97+74x^98+41x^100+32x^104+8x^108+4x^112+1x^116+1x^120+1x^136

The gray image is a code over GF(2) with n=352, k=12 and d=152.
This code was found by Heurico 1.16 in 2.52 seconds.