The generator matrix

 1  0  0  0  1  1  1  1  2  1 X+2  1  2  2  1  1  X  1  X  0  1  0  2  X  1  1  1  1  0  1 X+2  0  1  1  1  1 X+2  1  1  1  1  2  X  2  X  1  1  X  0  2  1  1  1  2 X+2  1  1  1  1  1  1  1  1  1  X  1  1  1  1  2  1  1  1  1  1  1  0  0  2  1  1  1  X X+2  X  2  1  1
 0  1  0  0  0  2  1  3  1  2  0 X+1  1  1 X+1 X+2  1  0  1 X+2 X+3  1  2  1 X+1 X+3  0  X  X  1  1  X  3  0  X X+3  1  1  X  2  3  2  1  1  X  1  2  0  0  X X+3  X  3  1  0  2  3  X  X X+2  2  3  2  1  1  1 X+2  1 X+3  1 X+1  X  0  0 X+3  1  1  1  0  1  3 X+2  1  X  2  1  X  X
 0  0  1  0  0  3  2  1  1  1  1  3  X X+3  2  2  2 X+3  3  1 X+3  X  1 X+3  X X+2  3  0  X X+1 X+2  1  2 X+1 X+3 X+3  3  1 X+3  X X+2  1 X+3  2  1  2  X  X  2  1 X+2  2 X+1  0  0 X+2  3 X+2  3  3  2  1 X+1 X+2 X+3 X+3  X X+3  2 X+1 X+3  X  1  2 X+3 X+1 X+2  1  1  3  3 X+1  0  1  2  1  2  X
 0  0  0  1  1  1  3  2  1  0 X+1  3 X+3 X+2  0 X+3  X  0 X+2  3  1  3  X X+3  1  2 X+3 X+2  1  2 X+1 X+2 X+3 X+2  1  0  1  3 X+1  X X+2  1  0  X  X X+2  2  1  1  3 X+1  3  1 X+2  1  3  0 X+3 X+3  3 X+1  3  X X+3  X  3  2  X  3  2  0 X+3  0  X  3 X+1  X X+1 X+2  X X+3  1 X+3  2  1 X+2  2 X+1
 0  0  0  0  X  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  0  2  0  2  X  X  X X+2 X+2  X X+2  X X+2  X  X X+2  X X+2  X  X  X X+2  2 X+2 X+2 X+2  2 X+2 X+2 X+2 X+2 X+2  X X+2  2  0  2  X X+2  X  X  X  2  0 X+2  X  2  X  2 X+2  2  X X+2 X+2 X+2  0  2 X+2  X  X  0 X+2  0

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+128x^79+469x^80+662x^81+771x^82+1026x^83+1143x^84+1146x^85+1208x^86+1364x^87+1219x^88+1138x^89+1195x^90+992x^91+957x^92+872x^93+630x^94+494x^95+405x^96+234x^97+113x^98+82x^99+54x^100+34x^101+16x^102+10x^103+4x^104+8x^105+1x^106+2x^108+2x^110+2x^112+2x^113

The gray image is a code over GF(2) with n=352, k=14 and d=158.
This code was found by Heurico 1.16 in 17.3 seconds.