The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1 X+2  1  1  0  1  1  0 X+2  1  1  1  0  1  1 X+2  1  1  1  X  0  1  1  0  1  1 X+2  1  0  1  1  1  1  1 X+2  X  1  0  1 X+2  1  1  1  1  2  1  1  1  1  X  1  1  1  1  2  X  1  1  1  X  1  1  1  2 X+2  1  2  X  0  1  1  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1  3 X+2  1  X  3  1  1 X+1  0 X+3  1  0  3  1 X+2  0 X+1  1  1  3 X+2  1  X X+1  1  3  1 X+2 X+1 X+1 X+2 X+1  1  1  3  1  X  1 X+3  0  0  2  1 X+1  3 X+3  X  1 X+2  X  2  1  1  1  2  3 X+3  1  X X+1  0  1  1  3  X  1  2  X X+2 X+1  3  1  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  2  2  2  0  0  0  2  2  2  2  0  2  0  2  0  0  2  0  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  2  0  2  0  0  0  2  2  0  2  2  0  0  2  0  2  2  0  0  2  2  2  0  2  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  0  2  2  0  2  2  2  0  2  0  2  0  0  0  0  2  2  0  0  0  0  2  2  2  2  0  0  2  0  0  2  2  2  0  0  0  0  2
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  0  0  2  0  0  2  0  2  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  2  2  2  0  2  0  2  2  2  2  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  0  2  2  2  2  0  2  0  2  0  2  2  2  2  0  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  0  0  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  2  0  2  2  0  2  2  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  2  0  0  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  0  0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  2
 0  0  0  0  0  0  0  2  0  2  2  0  0  2  0  2  2  2  0  2  0  2  0  0  0  0  0  0  2  0  2  0  2  2  2  0  2  2  0  2  0  0  0  0  2  0  2  0  2  2  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  2  0  2  0  2  0  2  2  2  2  2  0  0  2  0  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  2  0  0  2  0  2  2  0  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  0  2  0  0  2  0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  0  0  2  2  2  2  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+12x^77+65x^78+132x^79+147x^80+352x^81+333x^82+508x^83+288x^84+682x^85+511x^86+844x^87+478x^88+868x^89+513x^90+780x^91+256x^92+516x^93+268x^94+256x^95+81x^96+124x^97+67x^98+40x^99+6x^101+16x^102+26x^104+11x^106+3x^110+3x^112+4x^114+1x^118

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 10.6 seconds.