The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  1 X+2  1 X+2  1  1  2  1  1  1  0  1  1  X  1  X  1  2  1  1  1  2  1  2  1  1  1 X+2  1  1  0  1  1  1  X  2  X  1  1  1  1  1  1  X  1  0  1 X+2  1  1  1  1  1 X+2  1  1  1  X  2  1  X  X  1  2  1  1 X+2  0  X  1  1  0  1  1  1
 0  1  1  0 X+3  1  X X+1  1  3  1 X+2  0 X+3  1 X+3  1 X+2  1  1  2  X  1  1 X+3  0  1  0  1 X+3  1 X+2  1  2  1 X+2  1  X X+3 X+3  1  0  1  1 X+1  1  0  1  1  1  X  1 X+3  0  3 X+3  1 X+1  1  2  1 X+3  1  X X+2 X+1  1  X X+2 X+3  1  X  X  1  1 X+3  X X+1 X+2  1  2  2  0  X  2 X+3  3  0
 0  0  X  0 X+2  0  0  X  0 X+2  0  0  X  2 X+2  0 X+2  X  2  X X+2 X+2  0 X+2  X  2  0 X+2  X  2  2  0  X  2  0 X+2  X X+2  X  X X+2  X  2  2  0  2  X  X  X  X X+2  2  0 X+2  0  0  0  2  X  0  X X+2  0 X+2  2 X+2 X+2 X+2  0 X+2  0 X+2 X+2  0  2  2  0 X+2  2  X  2  X  2  2  X  2  X  X
 0  0  0  X  0  0  X  X  X  X X+2  2  X X+2 X+2  2  0  X  2  0  2  2 X+2  X  2  0 X+2 X+2  2 X+2  0  X  2 X+2  X X+2  2  0  2  0  X  2  X  2  2  2  0  2  X  X  2 X+2  X  X X+2  2  2  2  2 X+2  0  X  0  X  X X+2  X  2  0  2  X X+2 X+2 X+2  2  2  X  2 X+2 X+2  X  0  X  0 X+2 X+2  2  X
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  0  0  0  0  2  2  2  0  0  0  2  0  2  0  2  2  2  0  0  0  2  2  2  2  2  0  0  2  0  2  0  0  0  0  2  2  0  2  0  2  2  0  2  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  0  2  0  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  2  2  2  0  2  2  2  0  0  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  2  0  2  2  0  2  2  0  0  0  2  0  0  2  0  0  0  2  0  2  2  0  0  0  0  0  2  0  0  2  0  2  2  0  0  2  0  2  0  0  2  0  2  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  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  2  2  2  2  2  0  2  2  2  2  2  0  0  2  2  2  0  2  2  0  0  2  2  2  2  0  2  0  2  2  0  0  0  0  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  0  2  2  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  0  2  0  0  2  0  2  2  2  0  2  2  0  2  2  2  2  2  0  2  0  2  0  2  0  0  2  2  2  0  2  2  2  2  0  2  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+72x^77+162x^78+204x^79+512x^80+402x^81+854x^82+604x^83+1207x^84+874x^85+1603x^86+1034x^87+1653x^88+924x^89+1610x^90+792x^91+1266x^92+558x^93+698x^94+330x^95+392x^96+196x^97+154x^98+78x^99+65x^100+40x^101+29x^102+24x^103+17x^104+6x^105+4x^106+6x^107+6x^108+4x^110+1x^112+2x^114

The gray image is a code over GF(2) with n=352, k=14 and d=154.
This code was found by Heurico 1.16 in 52.7 seconds.