The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  X  1  2  1  1  1  1  0  1  1 X+2  1  1 X+2  1  1  2  2  1  1  0 X+2  0  1  1  1  1  1  1 X+2 X+2  1  1  1  1  0  1  1  X X+2  1  1  1  X  X  1  1  2 X+2  1  1  1  0  1  1 X+2  1  1  X  X  0  2  1  0  1  X  1  2  1  1  2 X+2  1  0  2  0  2  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1  0 X+3  2 X+3  1 X+2  1  1 X+2  1  1  0  0  1  1 X+1 X+1  1  1  1  3  2  3 X+3 X+1  2  1  1  X  X  2  1  1 X+2  1  1  1 X+3  X  X  1  1 X+1  X  1  1  X X+3  3  1  X  1  1  1 X+2  1  2  X  X  0  1  3  1  1  X  1  2  X  1  0  1  1  1  X  0
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  X  2  X  2  X  X  2  2  X X+2  2  2  0 X+2  0  0  X  X  0  0  0  0  2  2  X  0  X  X  X  2  2 X+2  X  X X+2  X  0  X  X  X X+2  0  0 X+2  2 X+2  X  X  2  2 X+2  2  0  X  X  0  0  0  0 X+2  X X+2  0  X  X X+2  2 X+2  0  2  X  0  0 X+2  2  0  X  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  2  0  2  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  0  2  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2  0  0  2  2  2  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  2  0  0  0  2  2  0  2  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  0  0  2  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  0  0  0  0  2  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  2  2  0  0  2  0  2  0  0  0  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  2  2  0  2  0  2  2  0  0  2  0  2  2  2  2  0  0  2  0  2  2  0  2  2  0  0  0  0  0  0  2  0  2  2  0  2  0  0  0  2  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  0  2  0  2  0  2  2  0  2  2  2  0  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  0  2  0  2  2  0  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+53x^76+84x^77+137x^78+270x^79+387x^80+482x^81+640x^82+898x^83+941x^84+1174x^85+1252x^86+1194x^87+1385x^88+1278x^89+1368x^90+1148x^91+943x^92+816x^93+525x^94+474x^95+306x^96+238x^97+119x^98+82x^99+58x^100+22x^101+34x^102+30x^103+15x^104+2x^105+14x^106+3x^108+4x^110+2x^112+3x^114+1x^116+1x^124

The gray image is a code over GF(2) with n=352, k=14 and d=152.
This code was found by Heurico 1.16 in 22.7 seconds.